The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
From inside the book
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Page 48
... square upon a given straight line . Let AB be the given ftraight line ; it is required to defcrib a fquare upon AB . E From the point A draw a AC at right angles to AB ; and make AD equal to AB , and through the point D draw DE parallel ...
... square upon a given straight line . Let AB be the given ftraight line ; it is required to defcrib a fquare upon AB . E From the point A draw a AC at right angles to AB ; and make AD equal to AB , and through the point D draw DE parallel ...
Page 56
... square of CB , is equal to the fquare of CD . Upon CD defcribe the fquare CEFD , join DE , and through B draw BHG parallel to CE or DF , and through H draw KLM parallel to AD or EF , and also through A draw AK parallel to CL or DM : And ...
... square of CB , is equal to the fquare of CD . Upon CD defcribe the fquare CEFD , join DE , and through B draw BHG parallel to CE or DF , and through H draw KLM parallel to AD or EF , and also through A draw AK parallel to CL or DM : And ...
Page 58
... square of AC : Therefore four times the rectangle AB , BC , together with the fquare of AC , is equal to the gnomon AOH and the fquare XH : But the gnomon AOH and XH make up the fi- gure AEFD which is the fquare of AD : Therefore four ...
... square of AC : Therefore four times the rectangle AB , BC , together with the fquare of AC , is equal to the gnomon AOH and the fquare XH : But the gnomon AOH and XH make up the fi- gure AEFD which is the fquare of AD : Therefore four ...
Page 61
... square of AG is double of the fquares of AC , CD : But the fquares of AD , DG are equal to the fquare of AG ; therefore the fquares of AD , DG are double of the fquares of AC , CD : But DG is equal to DB ; therefore the squares of AD ...
... square of AG is double of the fquares of AC , CD : But the fquares of AD , DG are equal to the fquare of AG ; therefore the fquares of AD , DG are double of the fquares of AC , CD : But DG is equal to DB ; therefore the squares of AD ...
Page 63
... square of BA is equal to the fquares of BC , CA , and twice the rectangle BC , CD ; that is , the fquare of BA is greater than the fquares of BC , CA , by twice the rectangle BC , CD . Therefore , in obtufe angled triangles , & c ...
... square of BA is equal to the fquares of BC , CA , and twice the rectangle BC , CD ; that is , the fquare of BA is greater than the fquares of BC , CA , by twice the rectangle BC , CD . Therefore , in obtufe angled triangles , & c ...
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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.