The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
From inside the book
Results 6-10 of 83
Page 65
... less than the fquares of AB , BC by twice the rectangle DB , BC . Laftly , Let the fide AC be perpendicular to BC ; then is BC the ftraight line between the perpendicular and the acute angle at B ; and it is manifeft that the fquares of ...
... less than the fquares of AB , BC by twice the rectangle DB , BC . Laftly , Let the fide AC be perpendicular to BC ; then is BC the ftraight line between the perpendicular and the acute angle at B ; and it is manifeft that the fquares of ...
Page 75
... less than DH : Therefore DG is the least , and DK less than DL , and DL than DH : Alfo there can be drawn only two equal ftraight lines from the point D to the circumference , one upon each fide of the leaft : At the point M , in the ...
... less than DH : Therefore DG is the least , and DK less than DL , and DL than DH : Alfo there can be drawn only two equal ftraight lines from the point D to the circumference , one upon each fide of the leaft : At the point M , in the ...
Page 77
... less than the greater , which is impoffible . Therefore the straight line which joins the points F , G cannot fall otherwife than upon the point A , that is , it must país through it . Therefore , if two circles , & c . QE . D. IF PROP ...
... less than the greater , which is impoffible . Therefore the straight line which joins the points F , G cannot fall otherwife than upon the point A , that is , it must país through it . Therefore , if two circles , & c . QE . D. IF PROP ...
Page 80
... less . Let ABCD de a circle , of which the diameter is AD , and centre E ; and let BC be nearer to the centre than FG ; AD is greater than any ftraight line BC which is not a diameter , and BC greater than FG From the centre draw EH ...
... less . Let ABCD de a circle , of which the diameter is AD , and centre E ; and let BC be nearer to the centre than FG ; AD is greater than any ftraight line BC which is not a diameter , and BC greater than FG From the centre draw EH ...
Page 81
... less than EK ; therefore the fquare of BH is greater than the fquare of FK , and the ftraight line BH greater than FK ; and therefore BC is greater than FG . Next , Let BC be greater than FG , BC is nearer to the cen- tre than FG , that ...
... less than EK ; therefore the fquare of BH is greater than the fquare of FK , and the ftraight line BH greater than FK ; and therefore BC is greater than FG . Next , Let BC be greater than FG , BC is nearer to the cen- tre than FG , that ...
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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.