## 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

Resultados 6-10 de 59

Página 150

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**construction**being made , because as BD to DA , so is CE to EA ; and as BD to DA , so is the triangle BDE to the triangle ADE ; and as CE to EA , so is the triangle CDE to the triangle ADE ; therefore the triangle BDE is to the triangle ... Página 151

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**construction**being made , because as BD to DC , fo is BA to AC ; and as BD to DC , so is BA to AEd , because AD is parallel to EC ; therefore BA is to AC , as BA to AE f . con- f . 11. 5 . sequently AC is equal to AE & , and the angle ... Página 152

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**construction**being made , because BD is to DC , as BA to AC ; and that BD is also to DC , as BA to AF ; therefore BA is to AC , as BA to AF f . wherefore AC is equal to AF % , and the angle AFC equal to the angle ACF , but the angle AFC ... Página 157

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**construction**being made , it may be proved in like manner that BC is equal to A D BG , and the angle at C equal to the angle BGC . but the an- G gle at C is not less than a right B CE angle ; therefore the angle F BGC is not less than a ... Página 165

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**construction**being made , because the rectangle con- tained by A , C is equal to the square of B , and the square of B is equal to the rectangle contained by B , D , because B is equal to Di therefore the rectangle contained by A , C is ...### Términos y frases comunes

alſo altitude angle ABC angle BAC baſe BC BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonſtrated deſcribed diameter drawn EFGH equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs likewife oppoſite parallel parallelepipeds parallelogram paſs perpendicular plane angles priſm PROP proportionals Propoſition pyramid rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhall be equal ſhewn ſide ſolid ſome ſpace ſphere ſquare of AC ſtraight line AC THEOR theſe thoſe thro triangle ABC vertex 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 1 - 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, fourths, &c.

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.