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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Σελίδα 8
... wherefore AL and BC are each of them equal to BG , and things that are equal to the fame are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
... wherefore AL and BC are each of them equal to BG , and things that are equal to the fame are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
Σελίδα 9
... wherefore alfo the point C fhall coin- cide with the point F , because the straight line AC is equal to DF . , but the point B coincides with the point E ; wherefore the bafe BC fhall coincide with the base EF . because the point B ...
... wherefore alfo the point C fhall coin- cide with the point F , because the straight line AC is equal to DF . , but the point B coincides with the point E ; wherefore the bafe BC fhall coincide with the base EF . because the point B ...
Σελίδα 25
... wherefore also the angle BCG is equal to the angle BCA , the lefs to the greater , which is impoffible . therefore AB is not unequal to DE , that is , it is equal to it . and BC is equal to EF ; therefore the two AB , BC are equal to ...
... wherefore also the angle BCG is equal to the angle BCA , the lefs to the greater , which is impoffible . therefore AB is not unequal to DE , that is , it is equal to it . and BC is equal to EF ; therefore the two AB , BC are equal to ...
Σελίδα 28
... wherefore if a straight line , & c . Q. E. D. C. 13. I. a . 29. I. b . 27. I. PROP . XXX . THEOR . TRAIGHT lines which are parallel to the fame ftraight line , are parallel to one another . S S Let AB , CD be each of them parallel to EF ...
... wherefore if a straight line , & c . Q. E. D. C. 13. I. a . 29. I. b . 27. I. PROP . XXX . THEOR . TRAIGHT lines which are parallel to the fame ftraight line , are parallel to one another . S S Let AB , CD be each of them parallel to EF ...
Σελίδα 34
... Wherefore triangles , & c . Q. E. D. a . 31. . TRI PROP . XXXVIII . THEOR . RIANGLES upon equal bases , and between the fame parallels , are equal to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and between ...
... Wherefore triangles , & c . Q. E. D. a . 31. . TRI PROP . XXXVIII . THEOR . RIANGLES upon equal bases , and between the fame parallels , are equal to one another . Let the triangles ABC , DEF be upon equal bases BC , EF , and between ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 73 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Σελίδα 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.
Σελίδα 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 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.
Σελίδα 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.