## 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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**fince**been of this opinion , as they thought it the moft probable . Sir Henry Savile , after the feveral arguments he brings to prove it , makes this conclufion ( Page 13. Prælect . ) " That , excepting a very few interpolations ... Página

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**fince**Theon's time hitherto . Befides , there are feveral other things , which have nothing of Euclid's accuracy , and which plainly fhew , that his Elements have been much corrupted by unfkilful geometers ; and , though thefe are not ... Página

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**fince**thefe Elements are the foundation of a fcience by which the investigation and difco- very of useful truths , at least in mathematical learning , is pro- moted as far as the limited powers of the mind allow ; and which likewife is ... Página 10

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**fince**it has been demonftrated that the whole . angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are alfo equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the ... Página 27

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**fince**they are parallel by the Hy pothesis . therefore the angle AGH is not unequal to the angle GHD , fition . that is , it is equal to it . but the angle AGH is equal to the angle b . 15. I. EGB ; therefore likewife EGB is equal 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.