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 11
... greater than the other . let AB be the greater , and from it cut off DB equal to AC , a . 3. 1 . the lefs , and join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC ...
... greater than the other . let AB be the greater , and from it cut off DB equal to AC , a . 3. 1 . the lefs , and join DC . therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two fides DB , BC ...
Σελίδα 12
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . again , because CB is e- A qual to DB , the angle BDC is equal a to the angle BCD ; but BDC has been proved to be greater than the fame BCD , which is ...
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . again , because CB is e- A qual to DB , the angle BDC is equal a to the angle BCD ; but BDC has been proved to be greater than the fame BCD , which is ...
Σελίδα 18
... greater than the angle ECF , there- fore the angle ACD is greater than BAE . in the fame manner , if the fide BC be bifected , it may be demonftrated that the angle d . 15. t . BCG , that is , the angle ACD , is greater than the angle ...
... greater than the angle ECF , there- fore the angle ACD is greater than BAE . in the fame manner , if the fide BC be bifected , it may be demonftrated that the angle d . 15. t . BCG , that is , the angle ACD , is greater than the angle ...
Σελίδα 19
... greater than the angles ABC , ACB . but ACD , ACB are together b equal to two right angles ; therefore the angles ... greater fide of every triangle is oppofite to the greater angle . TE Let ABC be a triangle of which the fide AC is ...
... greater than the angles ABC , ACB . but ACD , ACB are together b equal to two right angles ; therefore the angles ... greater fide of every triangle is oppofite to the greater angle . TE Let ABC be a triangle of which the fide AC is ...
Σελίδα 20
... greater than AB . wherefore the greater angle , & c . Q. E. D. See N. a . 3. I. b . 5. I. C. 19. I. See N. A PROP . XX . THEOR . NY two fides of a triangle ate together greater than the third fide . Let ABC be a triangle ; any two fides ...
... greater than AB . wherefore the greater angle , & c . Q. E. D. See N. a . 3. I. b . 5. I. C. 19. I. See N. A PROP . XX . THEOR . NY two fides of a triangle ate together greater than the third fide . Let ABC be a triangle ; any two fides ...
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.