The Elements of Euclid: Viz. the First Six Books, with the Eleventh and Twelfth. In which the Corrections of Dr. Simson are Generally Adopted, But the Errors Overlooked by Him are Corrected, and the Obscurities of His and Other Editions Explained. Also Some of Euclid's Demonstrations are Restored, Others Made Shorter and More General, and Several Useful Propositions are Added. Together with Elements of Plane and Spherical Trigonometry, and a Treatise on Practical GeometryJ. Pillans & sons, 1799 - 351 sider |
Fra bogen
Resultater 1-5 af 44
Side 110
... fame kind .. C. In a ratio , the first named magnitude is called the Antecedent Term , and the other the Confequent . V. The first of four magnitudes is said to have the same ratio to the fecond which the third has to the fourth , when ...
... fame kind .. C. In a ratio , the first named magnitude is called the Antecedent Term , and the other the Confequent . V. The first of four magnitudes is said to have the same ratio to the fecond which the third has to the fourth , when ...
Side 111
... ratio of that which it has to the fecond . XI . Of four continual proportionals , the firft is faid to have to the ... fame kind , the first is faid to have to the laft of them the ratio compounded of the ratio of the first to the fecond ...
... ratio of that which it has to the fecond . XI . Of four continual proportionals , the firft is faid to have to the ... fame kind , the first is faid to have to the laft of them the ratio compounded of the ratio of the first to the fecond ...
Side 115
... fame multiple of C that the whole DL is of F. For the fame reason , AG is the fame multiple of C that DH is of F. Wherefore , & c . Q. E. D. IF PROP . IV . THEOR . B L E € 2. 5 . I A C DF F the first of four magnitudes has the fame ratio ...
... fame multiple of C that the whole DL is of F. For the fame reason , AG is the fame multiple of C that DH is of F. Wherefore , & c . Q. E. D. IF PROP . IV . THEOR . B L E € 2. 5 . I A C DF F the first of four magnitudes has the fame ratio ...
Side 118
... fame ratio to the fame magnitude ; and the fame has the fame ratio to equal magnitudes . Let A and B be equal magnitudes , and C any other ; A has the fame ratio to C that B has to C ; and C has the fame ratio to A that it has to B 2 N ...
... fame ratio to the fame magnitude ; and the fame has the fame ratio to equal magnitudes . Let A and B be equal magnitudes , and C any other ; A has the fame ratio to C that B has to C ; and C has the fame ratio to A that it has to B 2 N ...
Side 119
... fame multiple of BC contains D ; therefore AB has to D Book V. a greater ratio than BC has to D. Alfo D has to BC a greater ratio than it has to AB . For , b7 . def . 5 . having made the same construction , take also MD the least mul ...
... fame multiple of BC contains D ; therefore AB has to D Book V. a greater ratio than BC has to D. Alfo D has to BC a greater ratio than it has to AB . For , b7 . def . 5 . having made the same construction , take also MD the least mul ...
Almindelige termer og sætninger
ABC is equal ABCD alfo alſo angle ABC angle ACB angle BAC arch bafe baſe becauſe the angle bifect Book XI cafe centre circle ABC circumference cofine confequently cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid exterior angle faid fame altitude fame manner fame multiple fame number fame ratio fame reaſon fecond fegment fhall fides fimilar firft firſt folid angle fome fore fquare fquare of AC fuperficies given ftraight line gnomon greater half the fum join lefs leſs Let ABC magnitudes meaſure oppofite angle pafs parallel parallelogram parallelopiped perpendicular plane angles prifm PROB propofition proportionals Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſhall ſquare tangent thefe THEOR theſe tiple triangle ABC Wherefore
Populære passager
Side 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 142 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 13 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 30 - ... then shall the other sides be equal, each to each; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, BCA equal to the angles DEF, EFD, viz.
Side 72 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Side 57 - If then the sides of it, BE, ED are equal to one another, it is a square, and what was required is now done: But if they are not equal, produce one of them BE to F, and make EF equal to ED, and bisect BF in G : and from the centre G, at the distance GB, or GF, describe the semicircle...
Side 145 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Side 48 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Side 35 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.