The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 sider |
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Side 174
... fimilar , and fimilarly fituated to a given rectilineal figure . Let AB be the given ftraight line , and CDEF the given rec- tilineal figure of four fides ; it is required upon the given ftraight line AB to defcribe a rectilineal figure ...
... fimilar , and fimilarly fituated to a given rectilineal figure . Let AB be the given ftraight line , and CDEF the given rec- tilineal figure of four fides ; it is required upon the given ftraight line AB to defcribe a rectilineal figure ...
Side 175
... fimilar to one another * . Next , Let it be required to defcribe upon a given straight line AB , a rectilineal figure fimilar , and fimilarly fituated to the rectilineal figure CDKEF . c I. def . 6 . Join DE , and upon the given ...
... fimilar to one another * . Next , Let it be required to defcribe upon a given straight line AB , a rectilineal figure fimilar , and fimilarly fituated to the rectilineal figure CDKEF . c I. def . 6 . Join DE , and upon the given ...
Side 176
... fimilar , and fimilarly defcribed triangle upoя the fecond . PROP . XX . THEOR . SIMILAR polygons may be divided into the same num- ber of fimilar triangles , having the fame ratio to one another that the polygons have ; and the ...
... fimilar , and fimilarly defcribed triangle upoя the fecond . PROP . XX . THEOR . SIMILAR polygons may be divided into the same num- ber of fimilar triangles , having the fame ratio to one another that the polygons have ; and the ...
Side 177
... fimilar , EB is to BA , as LG to GF ; and alfo , because the polygons are fimilar , AB is to BC , as FG to GH ; therefore , ex ae- quali 4 , EB is to BC , as LG to GH ; that is , the fides about d 22. 5 . the equal angles EBC , LGH are ...
... fimilar , EB is to BA , as LG to GF ; and alfo , because the polygons are fimilar , AB is to BC , as FG to GH ; therefore , ex ae- quali 4 , EB is to BC , as LG to GH ; that is , the fides about d 22. 5 . the equal angles EBC , LGH are ...
Side 178
... fimilar polygons , & c . Q. E. D. g 12. 5 . COR . 1. In like manner , it may be proved , that fimilar four fided figures , or of any number of fides , are one to another in the duplicate ratio of their homologous fides , and it has ...
... fimilar polygons , & c . Q. E. D. g 12. 5 . COR . 1. In like manner , it may be proved , that fimilar four fided figures , or of any number of fides , are one to another in the duplicate ratio of their homologous fides , and it has ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore
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Side 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Side 170 - 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 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Side 167 - 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 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.
Side 62 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Side 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Side 200 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 38 - 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.