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 |
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Resultat 1-5 av 100
Side 11
... join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the bafe DC ...
... join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the bafe DC ...
Side 13
... join DE , and upon it defcribe b an equilateral triangle DEF , then join AF . the straight line AF bifects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF are equal to ...
... join DE , and upon it defcribe b an equilateral triangle DEF , then join AF . the straight line AF bifects the angle BAC . Because AD is equal to AE , and AF is common to the two triangles DAF , EAF ; the two fides DA , AF are equal to ...
Side 14
... join FC . the ftraight line FC , drawn from the given point C , is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two tri- angles DCF , ECF ; the two fides AD 4 DC , CF are equal to the ...
... join FC . the ftraight line FC , drawn from the given point C , is at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two tri- angles DCF , ECF ; the two fides AD 4 DC , CF are equal to the ...
Side 18
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is b . 15. 1. equal to the angle CEF ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is b . 15. 1. equal to the angle CEF ...
Side 30
... join the extremities of two equal and parallel ftraight lines , towards the fame parts , are also themselves equal ... Join BC , and because AB is pa- rallel to CD , and BC meets them ; the alternate angles ABC , BCD C D A. 29. 1 . b . 4 ...
... join the extremities of two equal and parallel ftraight lines , towards the fame parts , are also themselves equal ... Join BC , and because AB is pa- rallel to CD , and BC meets them ; the alternate angles ABC , BCD C D A. 29. 1 . b . 4 ...
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Side 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.
Side 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.
Side 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Side 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.
Side 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.