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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Página 13
... PROP . IX . PROB . 10 bisect a given rectilineal angle , that is , to divide it into two equal angles . b . 8. Ax . Let BAC be the given rectilineal angle , it is required to bifect it . Take any point D in AB , and from AC cut off AE ...
... PROP . IX . PROB . 10 bisect a given rectilineal angle , that is , to divide it into two equal angles . b . 8. Ax . Let BAC be the given rectilineal angle , it is required to bifect it . Take any point D in AB , and from AC cut off AE ...
Página 17
... PROP . XV . THEOR . IT F two ftraight lines cut one another , the vertical , or oppofite , angles fhall be equal . Let the two ftraight lines AB , CD cut one another in the point E. the angle AEC fhall be equal to the angle DEB , and ...
... PROP . XV . THEOR . IT F two ftraight lines cut one another , the vertical , or oppofite , angles fhall be equal . Let the two ftraight lines AB , CD cut one another in the point E. the angle AEC fhall be equal to the angle DEB , and ...
Página 32
... PROP . XXXV . THEOR . ARALLELOGRAMS upon the fame bafe and between the fame parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the fame base BC and between the fame parallels AF , BC . the parallelogram ...
... PROP . XXXV . THEOR . ARALLELOGRAMS upon the fame bafe and between the fame parallels , are equal to one another . Let the parallelograms ABCD , EBCF be upon the fame base BC and between the fame parallels AF , BC . the parallelogram ...
Página 76
... PROP . XIX . F C GE THEOR . a . 18. 3 . See N. IF Fa ftraight line touches a circle , and from the point of contact a straight line be drawn at right angles to the touching line , the center of the circle fhall be in that line . Let the ...
... PROP . XIX . F C GE THEOR . a . 18. 3 . See N. IF Fa ftraight line touches a circle , and from the point of contact a straight line be drawn at right angles to the touching line , the center of the circle fhall be in that line . Let the ...
Página 79
... PROP . XXIII . THEOR . UPO PON the fame ftraight line , and upon the fame See N. fide of it , there cannot be two fimilar fegments of circles , not coinciding with one another . If it be poffible , let the two fimilar fegments of ...
... PROP . XXIII . THEOR . UPO PON the fame ftraight line , and upon the fame See N. fide of it , there cannot be two fimilar fegments of circles , not coinciding with one another . If it be poffible , let the two fimilar fegments of ...
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.