The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, to this Second Edition is Added the Book of Euclid's Data. In Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthR. and A. Foulis, 1762 - 466 Seiten |
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Seite 10
... alfo equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the ... alfo equiangular . PROP . VI . THEOR . IF two a be que oppofite to , the equal F two angles of a triangle be equal to ...
... alfo equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the ... alfo equiangular . PROP . VI . THEOR . IF two a be que oppofite to , the equal F two angles of a triangle be equal to ...
Seite 12
... alfo the bafe BC equal to the bafe EF . The angle BAC is e- qual to the angle EDF . For if the tri- angle ABC be ap- B plied to DEF fo СЕ F that the point B be on E , and the straight line BC upon EF ; the point C fhall alfo coincide ...
... alfo the bafe BC equal to the bafe EF . The angle BAC is e- qual to the angle EDF . For if the tri- angle ABC be ap- B plied to DEF fo СЕ F that the point B be on E , and the straight line BC upon EF ; the point C fhall alfo coincide ...
Seite 23
... alfo greater than the base EF . Of the two fides DE , DF let DE be the fide which is not greater n than the other , and at the point D in the straight line DE make a . 23. 1 . the angle EDG equal to the angle BAC ; and make DG equal bb ...
... alfo greater than the base EF . Of the two fides DE , DF let DE be the fide which is not greater n than the other , and at the point D in the straight line DE make a . 23. 1 . the angle EDG equal to the angle BAC ; and make DG equal bb ...
Seite 24
... alfo the third angle of the one to the third angle of the other . Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the angles DEF , EFD , viz . ABC to DEF , and BCA to EFD ; alfo one fide equal to one fide ; and ...
... alfo the third angle of the one to the third angle of the other . Let ABC , DEF be two triangles which have the angles ABC , BCA equal to the angles DEF , EFD , viz . ABC to DEF , and BCA to EFD ; alfo one fide equal to one fide ; and ...
Seite 25
... alfo the angle BCG is equal to the angle BCA , the less to the greater , which is impoffible . there- fore AB is not unequal to DE , that is , it is equal to it . and BC is e- qual to EF ; therefore the two AB , BC are equal to the two ...
... alfo the angle BCG is equal to the angle BCA , the less to the greater , which is impoffible . there- fore AB is not unequal to DE , that is , it is equal to it . and BC is e- qual to EF ; therefore the two AB , BC are equal to the two ...
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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 confequently conftruction cylinder defcribed demonftrated drawn equal angles equiangular equimultiples Euclid excefs faid fame multiple fame ratio fame reaſon fecond fegment fhall fhewn fides fimilar firft firſt folid angle fome fore fquare of BC given angle given in fpecies given in magnitude given in pofition given magnitude given ratio given ſtraight line gnomon greater join lefs leſs Let ABC likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular polygon prifms Propofition proportionals pyramid Q. E. D. PROP reafon rectangle rectangle contained rectilineal figure right angles ſhall ſphere ſquare ſtraight line AB thefe THEOR theſe thro tiple triangle ABC wherefore
Beliebte Passagen
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Seite 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Seite 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Seite 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Seite 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.