The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
From inside the book
Results 1-5 of 99
Page 82
... the circumference , which shall touch a given circle . First , Let A be a given point without the given circle BCD ; it is required to draw a ftraight line from A it 82 THE ELEMENTS Book III. Therefore the ftraight line drawn from A ...
... the circumference , which shall touch a given circle . First , Let A be a given point without the given circle BCD ; it is required to draw a ftraight line from A it 82 THE ELEMENTS Book III. Therefore the ftraight line drawn from A ...
Page 85
... First , Let E the centre of the circle be within the angle BAC , and join AE , and produce it to F : Becaufe EA is ... first cafe , that the angle GEC is double of the angle GDC , and that GEB a part of the first is double of GDB a ...
... First , Let E the centre of the circle be within the angle BAC , and join AE , and produce it to F : Becaufe EA is ... first cafe , that the angle GEC is double of the angle GDC , and that GEB a part of the first is double of GDB a ...
Page 120
... first has to the fecond . VIII . " Analogy , or proportion , is the fimilitude of ratios . ” IX . Proportion confifts in three terms at least . X. When three magnitudes are proportionals , the first is faid to have to the third the ...
... first has to the fecond . VIII . " Analogy , or proportion , is the fimilitude of ratios . ” IX . Proportion confifts in three terms at least . X. When three magnitudes are proportionals , the first is faid to have to the third the ...
Page 121
... first has the fame ratio to the third , which the fecond has to the fourth ; or that the first is to the third , as the second to the fourth : As is hown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion : When there ...
... first has the fame ratio to the third , which the fecond has to the fourth ; or that the first is to the third , as the second to the fourth : As is hown in the 16th prop . of this 5th book . XIV . Invertendo , by inversion : When there ...
Page 122
... first is to the laft of the others : Of this there are the two following kinds , which arife from the different ... first magnitude is to the fecond of the first rank , as the first to the fecond of the other rank ; and as the fe ...
... first is to the laft of the others : Of this there are the two following kinds , which arife from the different ... first magnitude is to the fecond of the first rank , as the first to the fecond of the other rank ; and as the fe ...
Other editions - View all
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.