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 twelfth |
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Page 253
... pyramid DEFH equal to one another , as the prism of which the bafe is the parallelogram KBXL and oppofite fide MO ... pyramid ABCG to the two prifms in the pyramid DEFH . and likewife if the pyramids now made , for example the two OMNG ...
... pyramid DEFH equal to one another , as the prism of which the bafe is the parallelogram KBXL and oppofite fide MO ... pyramid ABCG to the two prifms in the pyramid DEFH . and likewife if the pyramids now made , for example the two OMNG ...
Page 254
... pyramid ABCG to the two prifms in the pyramid DEFH ; and fo are the two prifms in the pyramid OMNG to the two prifms in the pyramid STYH ; and fo are all four to all four . and the fame thing may be shewn of the prifms made by dividing the ...
... pyramid ABCG to the two prifms in the pyramid DEFH ; and fo are the two prifms in the pyramid OMNG to the two prifms in the pyramid STYH ; and fo are all four to all four . and the fame thing may be shewn of the prifms made by dividing the ...
Page 255
... pyramid ABCG to any folid which is lefs than Book XII . the pyramid DEFH . in the fame manner it may be demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH to any folid which is lefs than the pyramid ABCG . Nor ...
... pyramid ABCG to any folid which is lefs than Book XII . the pyramid DEFH . in the fame manner it may be demonstrated , that the base DEF is not to the base ABC , as the pyramid DEFH to any folid which is lefs than the pyramid ABCG . Nor ...
Page 256
... pyramid FGHKLN . Divide the bafe ABCDE into the triangles ABC , ACD , ADE ; and the bafe FGHKL into the triangles ... pyramid ABCM to the pyramid FGHN ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid FGHN ...
... pyramid FGHKLN . Divide the bafe ABCDE into the triangles ABC , ACD , ADE ; and the bafe FGHKL into the triangles ... pyramid ABCM to the pyramid FGHN ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid FGHN ...
Page 257
... pyramid ABCDEM to the pyramid Book XII . FGHKLN . Therefore pyramids , & c . Q. E. D. PROP . VII . THEOR . Εν VERY prifm having a triangular base may be divided into three pyramids that have triangular bafes , and are equal to one ...
... pyramid ABCDEM to the pyramid Book XII . FGHKLN . Therefore pyramids , & c . Q. E. D. PROP . VII . THEOR . Εν VERY prifm having a triangular base may be divided into three pyramids that have triangular bafes , and are equal to one ...
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Common terms and phrases
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
Popular passages
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 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.
Page 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.
Page 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.