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 46
Side v
... solid angles are equal to one another which are contained by plane angles of the fame num- ber and magnitude , placed in the fame order ; but neither is this universally true , except in the case in which the folid angles are contained ...
... solid angles are equal to one another which are contained by plane angles of the fame num- ber and magnitude , placed in the fame order ; but neither is this universally true , except in the case in which the folid angles are contained ...
Side 6
... solids in the 11th Book so te- dious as is alledged : for if we omit the 22d , 23d , 26th , and 27th , together with all those after the 34th , as is usually done by the moderns , the rest are ftill accurately demonstrated without them ...
... solids in the 11th Book so te- dious as is alledged : for if we omit the 22d , 23d , 26th , and 27th , together with all those after the 34th , as is usually done by the moderns , the rest are ftill accurately demonstrated without them ...
Side 170
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles to a plane , when it makes right angles with every straight ...
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles to a plane , when it makes right angles with every straight ...
Side 171
... solid figures are such as are contained by the fame num- See N. ber of fimilar planes having the fame inclination to one an- other . X. Omitted . ΧΙ . A folid angle is that which is made by the meeting of more than two plane angles ...
... solid figures are such as are contained by the fame num- See N. ber of fimilar planes having the fame inclination to one an- other . X. Omitted . ΧΙ . A folid angle is that which is made by the meeting of more than two plane angles ...
Side 183
... solid angle be contained by three plane angles , any two of them are greater than the third . Let the folid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third . If the angles ...
... solid angle be contained by three plane angles , any two of them are greater than the third . Let the folid angle at A be contained by the three plane angles BAC , CAD , DAB . Any two of them are greater than the third . If the angles ...
Almindelige termer og sætninger
ABC is equal ABCD alſo altitude angle ABC angle ACB angle BAC arch baſe baſe BC becauſe the angle biſect cafe cauſe centre circle ABC circumference cofine conſequent conſtruction cylinder demonſtrated deſcribed diameter diſtance equal angles equiangular equimultiples Euclid exterior angle fame manner fame ratio fame reaſon fides fimilar firſt folid folid angle fore given ſtraight line greater half the ſum join leſs Let ABC magnitudes meaſure oppoſite parallel parallelogram parallelopiped paſs paſſes perpendicular plane angles priſm PROB propofition Q. E. D. PROP radius rectangle contained rectilineal figure remaining angle right angles ſaid ſame multiple ſame number ſecond ſegment ſhall be equal ſide ſolid ſome ſphere ſpherical triangle ſquare ſquare of AC ſtand ſuperficies THEOR theſe thoſe tiple triangle ABC uſed 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.