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 |
Inni boken
Resultat 1-5 av 21
Side 9
... sides of the one equal to two fides of the other , each to each , and have likewise the angles contained by thofe fides equal to one another ; their bafes fhall likewife be equal , and the triangles be equal , and their other angles to ...
... sides of the one equal to two fides of the other , each to each , and have likewise the angles contained by thofe fides equal to one another ; their bafes fhall likewife be equal , and the triangles be equal , and their other angles to ...
Side 13
... side of it there can be two triangles that have their fides which are terminated in one extremity of the base equal to one another , and likewife their fides terminated in the other extremity . but this is impoffible . therefore if the ...
... side of it there can be two triangles that have their fides which are terminated in one extremity of the base equal to one another , and likewife their fides terminated in the other extremity . but this is impoffible . therefore if the ...
Side 20
... BDC greater than the angle BAC . Produce BD to E ; and because two sides of a triangle are great- er than the third fide , the two fides BA , AE of the triangle ABE are greater than BE . to each of these add 20 ELEMENTS THE.
... BDC greater than the angle BAC . Produce BD to E ; and because two sides of a triangle are great- er than the third fide , the two fides BA , AE of the triangle ABE are greater than BE . to each of these add 20 ELEMENTS THE.
Side 41
... sides of AB , make with it at the point A the adjacent angles equal to two right angles ; therefore CA is in the fame ftraight lined with AG . for the same reason , AB and AH are in the fame ftraight line . and because the angle DBC is ...
... sides of AB , make with it at the point A the adjacent angles equal to two right angles ; therefore CA is in the fame ftraight lined with AG . for the same reason , AB and AH are in the fame ftraight line . and because the angle DBC is ...
Side 42
... side DC is equal to the fide BC . and because the fide DA is equal to AB , and AC common to the two triangles DAC , BAC , the two DA , AC are equal to the two BA , AC ; and the base DC is equal to the bafe BC ; therefore the an- gle DAC ...
... side DC is equal to the fide BC . and because the fide DA is equal to AB , and AC common to the two triangles DAC , BAC , the two DA , AC are equal to the two BA , AC ; and the base DC is equal to the bafe BC ; therefore the an- gle DAC ...
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.