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 |
Inni boken
Resultat 1-5 av 93
Side 12
... Parallel ftraight lines , are fuch as are in the fame plane , and which , being pro- duced ever fo far both ways , do not meet . PO L POSTULATES . I. ET it be granted that a 13 THE ELEMENTS Of four-fided figures, a fquare is that ...
... Parallel ftraight lines , are fuch as are in the fame plane , and which , being pro- duced ever fo far both ways , do not meet . PO L POSTULATES . I. ET it be granted that a 13 THE ELEMENTS Of four-fided figures, a fquare is that ...
Side 31
... parallel . Let the ftraight line EF , which falls upon the two flraight lines AB , CD , make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced , fhall ...
... parallel . Let the ftraight line EF , which falls upon the two flraight lines AB , CD , make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For , if it be not parallel , AB and CD being produced , fhall ...
Side 32
... parallel to CD . Wherefore , if a ftraight line , & c . Q. E. D. See the notes on this propo- fition . IF PROP . XXIX . THEOR . Fa ftraight line fall upon two parallel ftraight lines , it makes the alternate angles equal to one another ...
... parallel to CD . Wherefore , if a ftraight line , & c . Q. E. D. See the notes on this propo- fition . IF PROP . XXIX . THEOR . Fa ftraight line fall upon two parallel ftraight lines , it makes the alternate angles equal to one another ...
Side 33
... parallel to the fame ftraight line are parallel to one another . Let AB , CD be each of them parallel to EF ; AB is also parallel to CD . Let the ftraight line GHK cut AB , EF , CD ; and because GHK cuts the parallel ftraight lines AB ...
... parallel to the fame ftraight line are parallel to one another . Let AB , CD be each of them parallel to EF ; AB is also parallel to CD . Let the ftraight line GHK cut AB , EF , CD ; and because GHK cuts the parallel ftraight lines AB ...
Side 34
... parallel b to BC . Therefore the straight line EAF is drawn through the given point A parallel to the given ftraight line BC . Which was to be done . PROP . XXXII . THEOR . Fa fide of any triangle be produced , the exterior angle is ...
... parallel b to BC . Therefore the straight line EAF is drawn through the given point A parallel to the given ftraight line BC . Which was to be done . PROP . XXXII . THEOR . Fa fide of any triangle be produced , the exterior angle is ...
Vanlige uttrykk og setninger
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 avsnitt
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.