The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
From inside the book
Page 6
... shall be made evident in the Notes fubjoined to thefe Elements . In like manner , in the Demonftration of the 26th Prop . of the 11th Book , it is taken for granted , that thofe folid Angles are e- qual to one another which are ...
... shall be made evident in the Notes fubjoined to thefe Elements . In like manner , in the Demonftration of the 26th Prop . of the 11th Book , it is taken for granted , that thofe folid Angles are e- qual to one another which are ...
Page 43
... . IF a parallelogram and triangle be upon the fame base , and between the fame parallels ; the parallelogram shall be double of the triangle . Let 43 44 Book I. Let the parallelogram ABCD and the triangle OF EUCLID .
... . IF a parallelogram and triangle be upon the fame base , and between the fame parallels ; the parallelogram shall be double of the triangle . Let 43 44 Book I. Let the parallelogram ABCD and the triangle OF EUCLID .
Page 47
... shall be equal to a given rectilineal figure , viz . by applying to the given ftraight line , a parallelo- b 44. 1 . gram equal to the first triangle ABD , and having an angle e- qual to the given angle . PROP . Book T. a II . I. b 3. I ...
... shall be equal to a given rectilineal figure , viz . by applying to the given ftraight line , a parallelo- b 44. 1 . gram equal to the first triangle ABD , and having an angle e- qual to the given angle . PROP . Book T. a II . I. b 3. I ...
Page 62
... shall be equal to the fquare of the other part . a с G HB Upon AB defcribe the fquare ABDC ; bifect AC in E , and join BE ; produce CA to F , and make EF equal to EB ; and upon AF defcribe the fquare FGHA ; AB is divided in H fo , that ...
... shall be equal to the fquare of the other part . a с G HB Upon AB defcribe the fquare ABDC ; bifect AC in E , and join BE ; produce CA to F , and make EF equal to EB ; and upon AF defcribe the fquare FGHA ; AB is divided in H fo , that ...
Page 71
... shall cut it at right bangles ; wherefore FEB is a right angle : And FEA was fhewn to be a right angle ; therefore FEA is e- qual to the angle FEB , the lefs to the greater , which is im- poffible : Therefore AC , BD do not bifect one ...
... shall cut it at right bangles ; wherefore FEB is a right angle : And FEA was fhewn to be a right angle ; therefore FEA is e- qual to the angle FEB , the lefs to the greater , which is im- poffible : Therefore AC , BD do not bifect one ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.