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 - Trigonometry |
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Page 43
... contained by any two of the ftraight lines which contain one of the right angles . II . In every parallelogram , any ... rectangle contained . by the two straight lines , is equal to the rectangles contained by the undivided line , and ...
... contained by any two of the ftraight lines which contain one of the right angles . II . In every parallelogram , any ... rectangle contained . by the two straight lines , is equal to the rectangles contained by the undivided line , and ...
Page 44
... rectangle contained by the ftraight lines A , BC is equal to the rectangle contained by A , BD , B and to that contained by A , DE ; and alfo to that contained by A , EC . From the point B draw D. E. C BFG KL H A at right angles to BC ...
... rectangle contained by the ftraight lines A , BC is equal to the rectangle contained by A , BD , B and to that contained by A , DE ; and alfo to that contained by A , EC . From the point B draw D. E. C BFG KL H A at right angles to BC ...
Page 45
... rectangle contained by BA , AC ; for it is contained by Book II . DA , AC , of which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal to AB . therefore the rectangle contained by AB , AC together with the rectangle ...
... rectangle contained by BA , AC ; for it is contained by Book II . DA , AC , of which AD is equal to AB ; and CE is contained by AB , BC , for BE is equal to AB . therefore the rectangle contained by AB , AC together with the rectangle ...
Page 46
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB . and HF , CK are the fquares of AC , CB ; wherefore the four ...
... rectangle contained by AC , CB , for GC is equal to CB ; therefore GE is also equal to the rectangle AC , CB ; wherefore AG , GE are equal to twice the rectangle AC , CB . and HF , CK are the fquares of AC , CB ; wherefore the four ...
Page 47
... rectangle contained by the unequal parts , together with the fquare of the line between the points of fection , is equal to the fquare of half the line . Let the straight line AB be divided into two equal parts in the point C , and into ...
... rectangle contained by the unequal parts , together with the fquare of the line between the points of fection , is equal to the fquare of half the line . Let the straight line AB be divided into two equal parts in the point C , and into ...
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 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
Popular passages
Page 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.
Page 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.
Page 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.
Page 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 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.
Page 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.
Page 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 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.
Page 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.