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 páginas |
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Resultados 6-10 de 28
Página 336
... excess of A above B and C. then B , C , D together are greater than A ; and because A is greater than either B or C , much more will A and D , together with either of the two B , C be greater than the other . and , by the conftruction ...
... excess of A above B and C. then B , C , D together are greater than A ; and because A is greater than either B or C , much more will A and D , together with either of the two B , C be greater than the other . and , by the conftruction ...
Página 367
... excess of CD above a given magnitude has a given ratio to AB . Because the ratio of AE to CD is given , as AE to CD , fo make BE to FD ; therefore the ratio of BE to FD is given , and BE is given , wherefore FD is given . and because as ...
... excess of CD above a given magnitude has a given ratio to AB . Because the ratio of AE to CD is given , as AE to CD , fo make BE to FD ; therefore the ratio of BE to FD is given , and BE is given , wherefore FD is given . and because as ...
Página 368
... excess of the other above a given magnitude has to that one a given ratio ; or the other is given together with the magnitude to which that one has a given ratio . Let 1 Let the excess of the magnitude AB above a 368 EUCLID'S.
... excess of the other above a given magnitude has to that one a given ratio ; or the other is given together with the magnitude to which that one has a given ratio . Let 1 Let the excess of the magnitude AB above a 368 EUCLID'S.
Página 369
... excess of the magnitude AB above a given magnitude , have a given ratio to the magnitude BC ; the excess of AC , both of them together , above a given magnitude , has a given ratio to BC . Let AD be the given magnitude the excefs of AB ...
... excess of the magnitude AB above a given magnitude , have a given ratio to the magnitude BC ; the excess of AC , both of them together , above a given magnitude , has a given ratio to BC . Let AD be the given magnitude the excefs of AB ...
Página 370
... excess of AB above a given magnitude has a given ratio to BC . Let AE be the given magnitude ; and becaufe EB the excess of AB above AE has to AC a given ratio , as AC to EB , fo make AD d . 5. Dat . to DE ; therefore the ratio of AD to ...
... excess of AB above a given magnitude has a given ratio to BC . Let AE be the given magnitude ; and becaufe EB the excess of AB above AE has to AC a given ratio , as AC to EB , fo make AD d . 5. Dat . to DE ; therefore the ratio of AD to ...
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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 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
Pasajes populares
Página 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
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 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.
Página 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...
Página 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...
Página 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.
Página 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Página 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.
Página 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.
Página 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.