The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
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Page 10
... perpendicular to it . XI . An obtufe angle is that which is greater than a right angle . XII . An acute angle is that which is lefs than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is ...
... perpendicular to it . XI . An obtufe angle is that which is greater than a right angle . XII . An acute angle is that which is lefs than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is ...
Page 23
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given ftraight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
... perpendicular to a given straight line of an unlimited length , from a given point without it . Let AB be the given ftraight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ...
Page 63
... perpendicular falls , and the ftraight line intercepted without the triangle between the perpendicular and the obtufe angle . Let ABC be an obtufe angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ...
... perpendicular falls , and the ftraight line intercepted without the triangle between the perpendicular and the obtufe angle . Let ABC be an obtufe angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ...
Page 64
... perpendicular let fall upon it from the oppo- fite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its a- cute angles , and upon BC , one of the fides containing it , let fall the perpendicular AD from ...
... perpendicular let fall upon it from the oppo- fite angle , and the acute angle . Let ABC be any triangle , and the angle at B one of its a- cute angles , and upon BC , one of the fides containing it , let fall the perpendicular AD from ...
Page 65
... 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 AB , BC are e- qual to the fquare of AC , and twice the fquare of BC : Therefore , in every ...
... 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 AB , BC are e- qual to the fquare of AC , and twice the fquare of BC : Therefore , in every ...
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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.