## The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |

### From inside the book

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**fame ratio**are called proportionals , N. B. When four magnitudes are proportionals , it is • ufually expreffed by ... ratio than the third magni- tude has to the fourth ; and , on the contrary , the third is faid to have to the fourth a ... Page 121

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**fame ratio**which E has to F ; and B Book V. to C , the**fame ratio**that G has to H ; and C to D , the fame that K has to L ; then , by this definition , A is faid to have to D. the ratio compounded of ratios which are the fame with the ... Page 126

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**fame ratio**to the fecond which the third has to the fourth ; then any equimultiples whatever of the firft and third fhall have the**fame ratio**to any equimultiples of the fecond and fourth , viz . the equimultiple of the first shall have ... Page 127

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**fame ratio**to the fecond and fourth : And in like manner , the first and the third have the**fame ratio**to any equimultiples whatever of the second and fourth . Let A the firft , have to B the fecond , the**fame ratio**which the third C ... Page 129

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**fame ratio**which the third has to the fourth ; then , if the first be greater than the fecond , the third is alfo greater than the fourth ; and , if equal , equal ; if lefs , lefs . Take any equimultiples of each of them , as the ...### 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.