ANSWERS TO CORRESPONDENTS. Our readers will please to put last month for yesterday, p. 307, col. 2, line 28; and add s to nephew, line 48. J. FAULKNER (Smethwick): Man and mankind are general terms including every individual of the human race; male and female, young and old, servant and master, king and subject, negro and negro-driver.— J. J. NEWTON (Bridgewater): His solutions to the queries in No. 14, are nearly correct.-A. LEARNER (Greenock): His observations on Geometry are good: let him read our answer to J. S. (Ayrshire). His demonstration of the 47th B. I. contrary to his own maxim, depends on "Euc. B. I., 46, Cor. 2," by his own citation. This cor. is not Euclid's, but Dr. Thomson's, and even he refers to "Euc. B. I., 34, Cor. 2," for its demonstration; neither is the latter Euclid's, but Dr. Thomson's again, for he has added a demonstration. Euclid's demonstration is, therefore, on Learner's own showing, not complete. Neither is it on another ground; for, whichever of the six ways of constructing the diagram, a student happens to take, the demonstration ought to apply to that way; a thing which has not yet been satisfactorily made out on Euclid's principles, of the 47th.-A. ŠKERRIT (Holbrook): His solutions are correct, and very ingenious.-D. M. F. (Bradford) wishes us to put the following query: "How many acres of the earth's surface may be seen from the top of a steeple 400 feet high, the earth being perfectly spherical, and its diameter 7,920 miles."-LUPUS is right on the education of females of the middle class; it is preposterous. by A. W. (Edinburgh) wishes us to assist him in dividing z2+2+ a 1 x2 myself alone, but to be an example of perseverance and industry to my children and grandchildren." What a noble and praiseworthy feeling! It cannot, it will not, lose its reward.-PETER HAY (West Allerdean): E. FINIGAN (Manchester): Correct.-M. W. DICKSON (Dublin): Yes.-A WELL-WISHER, rates us soundly for using the subjunctive mood after the particle if!-NovI YELSOM (Manchester) makes the extraordinary request of us, to send him songs, "lively songs with choruses," in about 50 different languages, and he will discharge the debt in postage stamps!-G. H. CHELTENHAM, is right, Strabo was a Roman writer of Greek Geography-W. H. B. should study Cassell's Euclid, and the lectures in the P. E. together. Zumpt's Latin Grammar can be obtained of any respectable bookseller.-E. EVANS (Abergele): We cannot condescend to copy other people's plans in the management of our correspondence. Our earnest desire is to do ALL THE GOOD we can to EVERY INDIVIDUAL, believing that by so doing we shall benefit the mass in the long run; "a little leaven leaveneth the whole lump."-THOMAS KNOTT (Gateshead) is right; our religious readers should get "The Pathway;" therefore we send him to its editor for an answer to his religious question.-J. B. (Long Benton) should pronounce Montague thus: Mont-a-gue, with the emphasis on Mont, with the a short, the u long, and the e silent.-H. A. (Liverpool): In the French lessons, m. means masculine, and f. feminine.-MOLESTUS (Liverpool): The names of the cases in Latin shall be explained.-AN ASPIRANT to the profession of civil engineers, will ascertain how a person becomes a M. I. C. E. by calling at the institution, Great George-street, Westminster, and getting a copy of its rules and regulations.-C. F. P. (Dunmanway): we are obliged by his interesting communication. and shall keep it in view for the benefit of our readers. His solutions are correct.-A. SCOTSMAN is too wide an appellation; never mind the arrangement of the x First, put unity under the dividend to make a fraction of it; Latin words at present, if your translation be correct. You will see in the KEY, that the same sentence is arranged two or three different ways. -E. A. B. (Bellington): His solutions to the queries, p. 223, are very then invert the divisor, and multiply the two fractions together; the result good. No. 4. is a geometrical query.-J. M. L. (Edinburgh) wishes a a(x2+2+), 2x2-2x+1 will then be solution to the following query: Subtract from x-1 which can be reduced to its lowest terms. Bring the fractions to a common denominator by multiplying the terms This may be easily done by observing that the part of the numerator in a(x+2); 1 now by the denominator, the fraction in its lowest terms is for the answer in S. Y. B. (Tiverton): The method of putting down this sum in a ciphering-book is of little moment, provided the student shows that he thoroughly understands it. "From July 18th, 1823, to April 18th, 1850, how many years and days?" It might be done thus:Remaining days of 1823 Leap years from 1824 to 1848 inclusive ............ 166 days −1) (x-1) by cancelling like terms and x (x-1) dividing-H. E. his question has been answered.-AMICUS VERITAS Dictionary serve his purpose for a time.-H. B. (London): Spier's (Glasgow), who should have put VERITATIS, will find Entick's Latin French Dictionary is a very good one.-G. (Liverpool): correct.-J. H. (Shelton): Brande's Chemistry or Graham's.—ARITHMOS (Plymouth): the brick 9 inches long, 4 broad, and 2 thick, contains 101 cubic inches; for 9×40×21=1044.-GEORGE AUGUSTUS (Temple): the subject he proposes of inquiry into the meaning of proper names of persons, is both legitimate and interesting; but we doubt whether at the present stage of our progress, it would be acceptable to the majority of our readers, who seem more bent on the acquisition of positively useful 7 years knowledge, than upon that of the merely ingenious, entertaining and 19 years agreeable. In an old and valuable book, called Cruden's "Concordance 108 days. to the Holy Scriptures," you will find an explanation of the meaning of But if the all Scripture names, such as Michael; which by the way, is one of the names of the Lord Jesus Christ, he being the only archangel, or prince, chief, and ruler of angels. In some editions of Ainsworth's Latin Dictionary, you will find an explanation of non-scriptural names, such as Robert, &c. On the subject of surnames, there are also some books extant; the only one we remember at present is Buchanan on "Scottish Surnames;" and the Lowland Scots boast of a similar origin to the Saxons, repudiating, in the matter of ancient history, all connexion with the Gael.-AIA-KOPTOU (Fulham): Malte-Brun's or Mrs. Somerville's Physical Geography are among the best, and Lyell's Geology.-J. F. S. The one rule is that one noun governs another in the genitive whatever case the former may be in; and the other is that an active verb governs the accusative. Answer: 7 leap years, 19 common years, and 274 days. answer be required in days, thus :— A JERSEYMAN should read both the P. E. and the "French Lessons," A WARM FRIEND: If he will consult the previous chapter of the prophecies of Jeremiah, he will find that the princes of Judah took offence at the prophet's fidelity, and threw him into prison. Ebed-melech, an Ethiopian servant of Zedekiah, king of Judah, effected his release, and saved him from death by famine. To this pious and human man, the prophet was sent with a special message from God, and the words to which our friend refers in the close of the thirty-ninth chapter, are to be applied not to Jeremiah, but to Ebed-melech, and are meant to assure him of his personal safety in the midst of public calamity. As to the introduction of the name of NECHO in tho questions subjoined to the fourth lesson on Ancient History, it is simply a misprint, for the Apries or Pharaoh-Hophra of the text. 353 WE LESSONS IN PHYSIOLOGY. - No. IX. MAN. go on with our lesson on the nerves. You must keep in mind that the whole nervous system divides itself into distinct classes according to the functions or offices which the nerves have to perform. The following is the simplest arrangement which we can give :I. THE CEREBRO-SPI NAL NERVES, or those which have their root in the spine and the brain, and serve the purpose of sensation and motion. By far the greater number of the nerves which supply the body generally, arise from the spinal marrow, and are possessed of double power. This double power is owing to the subdivision of the nerve into two parts or roots. One root passes to the posterior portion of the this gives motion alone. THE EXCITO-MONERVES, or those which pursue their course from internal surfaces to the medulla oblongata or true spine, or that portion of the spinal marrow which in its ascent unites with the brain itself. These nerves are characterised by peculiar excitabilities; and when once excited pursue a reflex course from the medulla oblongata to the particular muscles on which they are designed to act,-the muscles concerned in the taking of food into the stomach, and then in throwing out whatever is not required for the nutrition and building up of the body. III. THE RESPIRATORY NERVES, or those which pass off from this same medulla oblongata, and diverge to different parts of the head, neck, throat, and chest, as the divinely-prepared mechanism Description of the Engraving. 1. Frontal branch of the fifth nerve of the brain which bestows sensation alone. II. Superior maxillary, or that branen of the fifth nerve which supplies the upper jaw, and which, like the last, arising from the sensitive root, bestows sensation alone. III. Mental or inferior maxillary branch of the fifth nerve. This also comes from the sensitive root. It is called mental, because it is involved in that expression which indicates the emotions of the mind. IV. Temporal branches of the same fifth nerve. They are distributed on the temples, and are for sensation. V. The only branch of the fifth nerve which arises from the smaller or motor root, and assists in the motion of those muscles which are employed in mastication or chewing. VI. VII. VIII. IX. These are spinal nerves; the first of the series which come out between the vertebræ, in the whole length of the spine, to supply the body generally with motion and sensation. A. The facial nerve. It is situated in the front of the ear, and is the VOL. I. for respiration, and to which, as the organ of speech, voice, and expression, man owes so much of his superiority to all other portions of this earthly creation. IV. THE GANGLIONIC OR SYMPATHETIC NERVES, or such as unite in sympathy those organs of the body by which the various organic functions are performed:-such as secretion, absorption, assimilation of the food, and so on. Now as no animal can be compared with man in the number and range of his faculties, so there is not one which approaches him in the development and perfection of his nervous system. The connexion between this nervous system and the brain is very close; and not less close is the relation between the brain and the mind. The mind becomes conscious of external objects only by the influence which they exert on that part of the brain which is called THE SENSORIUM, from its being the peculiar seat of sensation. An impression is made upon any part of the surface of the body by mechanical contact, by heat, by electricity, or by any other external agent; this impression is conveyed by the nervous system to the sensorium, a certain change takes place in the condition of the brain, and the impression is then said to be felt, that is to say, the mind becomes conscious of it. Now it is not the impression made on some remote organ of the body by which the mind is influenced, but simply and immediately by the change which has taken place in the brain. This admits of easy proof. Let us sup motor nerve of the features. It sends branches (a) to the muscles of the forehead and eyebrows. Branches (b) to the eyelids. Branches (c) to the muscles which move the nostrils and upper lip. Branches (d) to the lower lip. Branches (e) going down to the side of the neck. Connexions (f) with the spinal nerves of the neck. A nerve (g) to a portion of the muscle that is in the back of the head, and to muscles of the ear. B. The nervus vagus, or the wandering nerve, so named from its exten sive distribution. This is the grand respiratory nerve. C. The spinal accessory nerve. D. The ninth nerve, which is the motor nerve of the tongue. E. The nerve which supplies the diaphragm. F. Branch of the sympathetic nerve. G. A branch of the nervus vagus, which goes to the superior portion of the larynx or windpipe. * H. Another branch of the vagus, which goes to the inferior portion of the larynx. I. The nerve which goes to the tongue and upper part of the gullet called the pharynx. 23 pose, as is really the case, that the mind remains perfectly capable sensations. It is common to nearly the whole surface of the body; ul receiving any impression, but that all communication with the but nowhere is the sensibility so keen or acute as at the end of the brain is cut off. What is the consequence? Let the pressure fingers. The following cut shows the distribution of the nerves of which is applied to any distant part of the nervous system be what touch at the extremity of the thumb; It may, no impression is felt, we have no consciousness of it. For example:-"The surface of the eye-a part so exquisitely sensible, that if a fine hair touches it, there will be severe pain and spasm of the eyelids-may, when the nerve is destroyed, be rudely pressed with the finger, and the patient will nevertheless be unconscious of pain; or, if the surface be inflamed, and it be necessary to scarify it with the point of the lancet, in order to withdraw blood, the patient will submit to the operation without pain, and without even winking, although the eyelids retain their power of closing." It flows from this, that in the process by which the mind is rendered cscious of external objects, there are three distinct steps or stages : i. The reception of the impression which is made at the extremity of the nerve of sensation. ii. The conducting of this impression along the trunk of the norve to the sensorium or the brain. ii. The change excited by this impression in the sensorium itself, arough which sensation is produced. The sensitive extremities of the cerebro-spinal nerves transmit all their impressions to the brain under the form of sensations. "Although we commonly refer our various sensations to the parts at which the impressions are made; as, for instance, when we say that we have a pain in the hand, or an ache in the leg, we really use incorrect language; for though we may refer our sensations to the parts where the impression is first made on the nerves, they are really felt in the brain. This is evident from two facts :-first, that if the nervous communication between the part and the brain de interrupted, no impressions, however violent, can make themselves felt; and, second, that if the trunk of the nerve be irritated or pinched anywhere in its course, the pain which is felt is referred, not to the point injured, but to the surface to which these nerves are distributed. Hence the well-known fact, that for some time after the amputation of a limb, the patient feels pains which he refers to the fingers or toes that have been removed. This continues until the irritation of the cut extremities of the nervous trunks has subsided." and the human hand, both by reason of touch or resistance. Its chief purpose is to direct animals in their choice of food, and hence the wisdom of placing its organ at the entrance to the digestive canal. The sense of taste is of a much more refined nature than that of touch; but, like that of touch, is excited by direct contact with particular substances. This contact produces either an agreeable or a disagreeable sensation. The savour may be strong, or slight, or insipid, and the impression will correspond. But the impression produced by every substance taken into the mouth, depends as much on smell as on taste. If you take some decidedly aromatic body into the mouth, and press the nostrils close together, you will scarcely be conscious of any taste. Withdraw the pressure from the nostrils, and leave their passage perfectly free, and immediately you become conscious of a certain impression or sensation. But while there is this common sensibility which is diffused over the greater part of the body, there are organs of special sense, endowed with the property of receiving impressions peculiar to themselves. These senses are five-touch, taste, smell, sight, and hearing-while the impressions derived from them not only differ from all our other sensations, but differ the one from the other. The sense of touch would never give us the idea or knowledge of those properties which are discovered by taste; nor would the idea of form, shape, or bulk, ever be derived from the sense of smell. The eye would never distinguish sounds, nor would the ear ever | Jiscriminate colours. Who would ever think of saying that he hears a beautiful flower, or sees an enchanting sound, or smells a square body, or grasps a disagreeable odour? Each sense has its own nerve, and though "we can acquire a knowledge of the shape and position of objects by the touch, we could ferm no notion of their colour without sight, of their sounds without hearing, or of their odours without smell." Have, then, these nerves of special sense nothing in common? Are they not all susceptible of impressions inseparable from a feeling of pain? It cannot be denied that any violent or excessive impression may occasion a certain degree of discomfort. For example:-The effect of strong dazzling light, or of any sudden unexpected sound, or of any powerful odour, or of any very decided taste, would be followed by corresponding uneasiness. But mark, this is only a question of degree. These very sensations, in a more or less degree, might afford a certain pleasure or delight, or even in the same degree in a different condition of the body. Our feeling of pleasure or of pain very much depends on the previous condition of the part affected, as also upon the extent of surface on which an impression is made. For example:-If you put one hand in hot water, and the other in cold, and then transfer both to tepid water, this tepid water will seem cool to the one, and warm to the other. The second fact may be proved thus :-Hot water, into which you might introduce a single HEARING.-The ear presents a very beautiful, but very complifinger without any unpleasant sensation, would, on plunging the cated apparatus. With the form and the situation of the external whole hand into it, not only scald the hand, but give you the feel-ear you are already familiar. The apparatus more properly coning of pain. sists of the tympanum or drum, with its membrane and chain of TOUCH is the most general and the most diffused of our external benes; and which is adapted to direct itself, more or less com SMELL. If the thousand varieties of savour, may, in relation to the sense of taste, be all resolved into agreeable and disagreeable, then analogous characters pertain to those various odours, which, in relation to the sense of smell, are either pleasant or repugnant. This sense of smell depends upon the diffusion of the particles of the substance through the surrounding air, in a state of extreme minuteness. These particles proceeding or flying off from larger bodies, take on a certain degree of volatility, and coming into contact with the mucous membrane which lines the nasal cavities, and in which the olfactory nerve is distributed, we become conscious of a corresponding sensation. The atmospheric air, in its passage through the nostrils, is, during inspiration, the vehicle of those odorous particles into the olfactory organ, and by coming into immediate contact with its mucous membran, informs the animal of the presence, at a greater or less distance, of the bodies which are the source of these odours. In proportion to the extent of this membraneous surface, is the acuteness of the sense. In this respect man is far surpassed by many of the lower animals. that membrane. Beyond the membrane is this auditory cavity, which is filled with the air which it receives through the Eustachian tube; and behind this cavity, and opposite to the membrane of the tympanum, is a membrane of the same kind with two apertures, the one oval, and the other round, and these two membranes are united by a chain of little bones. The vibrations produced in the membrane of the tympanum, are transmitted to the membrane with the oval aperture by means of this little chain of bones, from the air contained within the osseous walls of the cavity. This cavity, again, is in communication with the vestibule, which borders upon a system of semicircular canals, which together form the labyrinth or internal ear. These canals contain a watery liquid, into which the fibres of the auditory nerve plunge. The vibrations of the membrane with its apertures are transmitted hither; and the nerve conveying these impressions to the brain, we have the sensation of hearing. SIGHT. The eye, as the organ of vision, is made up of an assemblage of parts even more complex than those of the ear. It is an optical instrument of wonderful completeness. This beautiful instrument presents the form and appearance of a globe, and consists of a spheroidal envelope-THE SCLEROTIC-which offers to its anterior part, a transparent circular segment-THE CORNEA-for Crystalline lens. the passage of the rays of light,-and to its posterior portion, a round opening for the introduction of the optic nerve, which at once developes itself in a nervous membrane-THE RETINA-doubling within the sclerotic in a manner to curtain three-fourths of the posterior of the spheroidal cavity of the globe. It is upon this nervous expansion that the luminous rays fall, and penetrating through it, terminate upon an absorbent membrane, impregnated with a black matter. This membrane is named THE CHOROID, and is that coat which is found immediately under the sclerotic. At the level of the union of the cornea with the sclerotic, the cavity of the eye is separated into two parts by a moveable, vertical, and diversely-coloured partition-THE IRIS-which is pierced in the centre by a round opening-THE PUPIL. The anterior parts of the cavity of the eye is filled by a transparent liquid-THE AQUEOUS HUMOUR. The posterior part contains THE CRYSTALLINE LENS; situated behind the iris, enclosed in a concavity of the vitreous body, which is a transparent mass made up of little cells full of watery liquid, and this liquid fills all the posterior cavity, even to immediate contact with the retina, Through the various transparent media of the cornea, the aque ous humour, the crystalline lens, and the vitreous body, the sys of light which diverge from the several points of any object, must pass to reach the retina. Falling upon the front of the cornea, they are refracted by its convex surface, while passing through it into the eye. Here they slightly converge; but are brought more closely together by the crystalline lens, which they reach after passing through the pupil. The refracting influence of the lens, together with that produced by the aqueous humour, is such as to bring these rays to a focus on the retina, where is formed a complete inverted image of the object. Then to prevent the light that forms the picture from being reflected from one part of the interior of the globe to another, which would mar and confuse the picture, the retina, which is almost transparent, is spread over the layer of black pigment which lines the choroid coat, and is designed to absorb the rays as soon as they have passed through the retina. The impression of the image is then transmitted by the optio nerve to the brain, and we become conscious of a certain sensation. According to Sir Charles Bell's theory and arrangement, the distribution of the nerves to the face and neck is seen in the figure p. 353. An arrangement this which again proclaims the infinite skill and love of Him whose hands fashioned our wondrous frame, and in whom we live, and move, and have our being. Which are the organs of special sense? Which is the grand distinguishing organ of touch in man? Describe how we get our impression of objects by the sense of sight. How are the rays of light kept from being reflected from one part of the globe of the eye to another? Where are the nerves of voice and expression distributed? Is there any animal which approaches man in the development and perfection of his nervous system? What feelings should this awaken in us towards the great Creator? LESSONS IN LATIN.-No. XXI. By JOHN R. BEARD, D.D. REGULAR VERBS. THE SECOND CONJUGATION. ACTIVE VOICE. Chief Parts; moneo, monui, monitum, monére. THE Corresponding parts and signs having been given under the first conjugation, need not be repeated; in the Latin, the student will easily make the alterations required by the difference of conjugation, and the English is unaffected by conjugation. MOODS, TENSES, &c. OF MONEO, I remind. Subjunctive. Imperative. Infinitive. Particip Indicative. Participle. ceas; timebam ne inimícus mihi noceret; timuit puer ne tacuerit mater; curabam ut pueri mores emendarem et corpus exercerem curabam ut pueri mores emendares et corpus exerceres; curabam ut praeceptor pueri mores emendaret et corpus exerceret; timee ut venias; timet maritus ne uxor occidat; timuit praeceptor na discipulus ejus verbis pareret; malus puer timet ut veniat praeceptor. 1. Monitum 2. Monitu ENGLISH-LATIN. He reminded me; they reminded the king; I might remind you; you might remind me; they have reminded the boy; thou wast reminding the woman; I will remind the teacher; be silent; do you be silent; let them be silent; the woman was suddenly silent; take care to improve; that thou improvest the morals of the citizens; I fear he may displease thee; the boys feared to displease their father; he pleases all (persons); a good man will displease the bad; why art thou silent? they fear that Caesar will conquer their country; good sisters fear (their) brothers will not be well; art thou well? I fear thou wilt not be well; if thou exercisest thy body thou wilt be well; my mother fears an entrance into heaven will (may) not lie open to me. In reply to some inquiring correspondents, the following information is added to the subject of nouns : EXERCISES:-Like moneo form doceo, I teach; and habeo, tive points out that which is caused (causa) or effected, that I have. VOCABULARY. Exerceo 2, I exercise; gaudeo 2, I rejoice; gaudeo quod, I rejoice that; valeo 2, I am well; pareo 2, 1 obey; placeo 2, I please; displiceo 2, 1 displease; oblivio, ónis, f. forgetfulness; deleo 2, I blot out; floreo 2, I flourish; probe, honestly, properly; taceo 5, I am silent (E. R. tacit); repente, adv. suddenly; aditus, ûs, m. access, entrance (E. R. an adit); pateo 2, I lie open, I am open; timeo 2, I fear (E. B. timid); noceo 2, I injure; venio 4, I come; occido 3, I fall, die. Observe that, occasionally, forms of other conjugations, &c., than the one immediately under treatment, are introduced with a view to keep up the student's attention, exercise his ingenuity, and test his progress. RULE.-After verbs expressive of fear, ne is used with the subjunctive of the following verb. Ne is, in Latin, a negative, and may be often rendered by lest; it may, however, in construing into English, be altogether dropped, the ordinary connecting particle that, or that not, being put between the two verbs; e. g., Exerceo; exercebam; exercebat; exercebo; gaudeo quod tu vales; præceptor gaudebat quod vos ejus præceptis parebatis; tibi placebas, aliis displicebas; virtutis honorem nulla oblivio delebit; exercui; Græcia omnibus artibus floruit; laudo vos quod mentes veras studio probe exercuistis; cur tacuistis? Tacuit puer reperte; tacebat mater; tacent omnes; nisi virtutis præcep is, parueritis, aditus in coelum vobis non patebit; si cupiditates tuas coercueris, beatus eris; curo ut pueri mores emendem et corpus exerceam; moneo vos ut patris praecepta observetis; timebam ne vobis displicerem; cura ut pueri mores emendes et corpus exer The names of the cases in Latin are of Greek origin, as is the term case (ptosis, fall) itself. The nominative is so called because it assigns the name (nomen) of the agent; the genitive denotes the relation of genus, origin or birth, that out of which a thing arises, and to which therefore it belongs; the accusawhich receives the action implied in the verb, the result of that action, the object or thing on which the action falls; the dative case is the giving (do, dare, dedi, datum, to give) case, signifying the person (or thing) to which something is given or assigned; the vocative (voco, I call) is the case of calling on or addressing; and the ablative (ablatus, taken from)_bears the name because it involves the idea of separation. In the Greek there is no ablative, the relations implied in that case being expressed partly by the genitive, partly by the dative. LESSONS IN GEOMETRY.-No. X. DEFINITIONS. BOOK I. FROM VIII. TO XII. INCLUSIVE. VIII. [A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.] This definition is put in brackets, as useless, and unnecessary to be remembered. IX. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. When two straight lines meet at a point, so that if produced they would intersect (cross) each other, the indefinite space between them is called an angle. B A D N.B. "When several angles are at one point B, anyone of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these two is somewhere upon one of those straight lines, and the other upon the other straight line: thus the angle which is contained by the straight lines, A B, C B, is named the angle ABC, or C BA; that which is contained by AB, DB, is named the angle A B D, or D BA; and that which is contained by DB, CB, is called the angle D B C, or CBD; but, if there be only one angle at a point, it may be expressed by a letter placed at that point; as the angle at E." This explanation is put in inverted commas, as being Dr. Simson's addition; it is very necessary to be remembered. X. When a straight line standing on another straight line makes the adjacent angles equal to one another, each of these angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. By borrowing the terms vertical and horizontal from the language of Physics, we may define a right angle to be that which is formed by the meeting of a vertical and horizontal line. L |