## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The first six books, together with the eleventh and twelfthF. Wingrave, 1804 |

### Dentro del libro

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Página 118

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**ratio**to the fecond which the third has to the fourth ; then any equimultiples whatever of the firft and third fhall ...**because**E is the fame multiple of A , that F is of C ; and of E and F have been taken equimultiples K , L ... Página 123

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**because**A is to B ,**as**C is to D ; and of B the second and D the fourth equimul- tiples have been taken E and F ; A ...**ratio**to the fame magnitude ; and the fame has the fame**ratio**to equal magnitudes . Let A and B be equal magnitudes ... Página 127

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**because**A has a greater**ratio**to C , than B has to C , there are a fome equimultiples of A and B , and fome multiple of a . 7.Def . 5 . C fuch , that the multiple of A is greater than the multiple of C , but the multiple of B is not ... Página 129

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**because**if there be any number of magnitudes equimultiples of**as**many , each of each , whatever multiple one of them ...**ratio**which the see Ni third has to the fourth , but the third to the fourth a greater**ratio**than the fifth has to ... Página 130

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**ratio**to B , than a . 7.Def . 5. E has to F 2. Wherefore if the firft , & c . Q. E. D. See N. a . 8. 5 . COR . And ...**Because**A is greater than C , and B is any other magnitude , A has to B a greater**ratio**than C to B a . but**as**A is to ...### Términos y frases comunes

alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe circle ABCD circumference cone conſtruction cylinder defcribed demonſtrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fecond fegment fhall fhewn fides fides BA fimilar fince firft firſt folid angle fore fquare fquare of AC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular plane angles PROP Propofition pyramid rectangle contained rectilineal figure right angles ſame ſhall ſpace ſphere ſquare ſtraight line AB THEOR theſe thro tiple triangle ABC wherefore

### Pasajes populares

Página 157 - D ; wherefore the remaining angle at C is equal to the remaining angle at F ; Therefore the triangle ABC is equiangular to the triangle DEF. Next, let each of the angles at C, F be not less than a right angle ; the triangle ABC is also, in this case, equiangular to the triangle DEF.

Página 24 - ... be equal, each to each ; and also the third angle of the one to the third angle of the other. Let ABC, DEF be two triangles which have the angles ABC, ECA equal to the angles DEF, EFD, viz.

Página 45 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Página 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Página 163 - 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.

Página 81 - ELF. Join BC, EF ; and because the circles ABC, DEF are equal, the straight lines drawn from their centres are equal: therefore the two sides BG, GC, are equal to the two EH, HF ; and the angle at G is equal to the angle at H ; therefore the base BC is equal (4.

Página 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Página 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Página 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.