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 sider |
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Resultater 6-10 af 74
Side 18
... less than two right angles . Produce BC to D ; and be- caufe ACD is the exterior angle of the triangle ABC , ACD is * than the interior and oppofite angle ABC ; to each of 4. 15. 1. greater A B C D thefe thefe add the angle ACB ...
... less than two right angles . Produce BC to D ; and be- caufe ACD is the exterior angle of the triangle ABC , ACD is * than the interior and oppofite angle ABC ; to each of 4. 15. 1. greater A B C D thefe thefe add the angle ACB ...
Side 19
... less than two right angles . therefore any two angles , & c . Q. E. D. TH PROP . XVIII . THEOR . HE greater fide of every triangle is oppofite to the greater angle . Let ABC be a triangle of which the fide AC is greater than the fide AB ...
... less than two right angles . therefore any two angles , & c . Q. E. D. TH PROP . XVIII . THEOR . HE greater fide of every triangle is oppofite to the greater angle . Let ABC be a triangle of which the fide AC is greater than the fide AB ...
Side 20
... less than the other two fides of the triangle , but hall contain a greater angle . Let the two ftraight lines BD , CD be drawn from B , C , the ends of the fide BC of the triangle ABC , to the point D within it . BD and DC are lefs than ...
... less than the other two fides of the triangle , but hall contain a greater angle . Let the two ftraight lines BD , CD be drawn from B , C , the ends of the fide BC of the triangle ABC , to the point D within it . BD and DC are lefs than ...
Side 24
... less D b . 24. 1 . b than the bafe EF ; but it is not ; therefore B C E F the angle BAC is not lefs than the angle EDF . and it was fhewn that it is not equal to it ; therefore the angle BAC is greater than the angle LDF . Wherefore if ...
... less D b . 24. 1 . b than the bafe EF ; but it is not ; therefore B C E F the angle BAC is not lefs than the angle EDF . and it was fhewn that it is not equal to it ; therefore the angle BAC is greater than the angle LDF . Wherefore if ...
Side 25
... 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 DE , EF , each to each ; and the angle ABC is equal ...
... 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 DE , EF , each to each ; and the angle ABC is equal ...
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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
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Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
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 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.
Side 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...
Side 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...
Side 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.
Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.
Side 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.