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 σελίδες |
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Αποτελέσματα 6 - 10 από τα 18.
Σελίδα 264
... cone , and so on , there muft at length remain fome fegments of the cone which toge- ther fhall be less than the excess of the cone above the third part of the cylinder . let thefe be the fegments upon AE , EB , BF , FC , CG , GD , DH ...
... cone , and so on , there muft at length remain fome fegments of the cone which toge- ther fhall be less than the excess of the cone above the third part of the cylinder . let thefe be the fegments upon AE , EB , BF , FC , CG , GD , DH ...
Σελίδα 265
... cone † , the pyramid inscribed in the cone is half Book XII . of the pyramid circumfcribed about it , because they are to one ano- ther as their bases . but the cone is less than the circumfcribed py- a . 6. 12 . ramid ; therefore the ...
... cone † , the pyramid inscribed in the cone is half Book XII . of the pyramid circumfcribed about it , because they are to one ano- ther as their bases . but the cone is less than the circumfcribed py- a . 6. 12 . ramid ; therefore the ...
Σελίδα 266
... cone , viz . the pyramid of which the base is the polygon EOFPGRHS , and its vertex the fame with that of the cone , is greater than the folid X. In the circle ABCD defcribe the polygon ATBYCVDQ_fimilar to the polygon EOFPGRHS , and ...
... cone , viz . the pyramid of which the base is the polygon EOFPGRHS , and its vertex the fame with that of the cone , is greater than the folid X. In the circle ABCD defcribe the polygon ATBYCVDQ_fimilar to the polygon EOFPGRHS , and ...
Σελίδα 267
... cone AL to any folid which is less than Book XII . the cone EN . In the fame manner it may be demonftrated that the circle EFGH is not to the circle ABCD , as the cone EN to any fo- lid less than the cone AL . Nor can the circle ABCD be ...
... cone AL to any folid which is less than Book XII . the cone EN . In the fame manner it may be demonftrated that the circle EFGH is not to the circle ABCD , as the cone EN to any fo- lid less than the cone AL . Nor can the circle ABCD be ...
Σελίδα 268
... cone EFGHN . First , let it have it to a less , viz . to the folid X. make the fame conftruction as in the preceeding Propofition , and it may be demonftrated the very fame way as in that Propofition , that the pyramid of which the base ...
... cone EFGHN . First , let it have it to a less , viz . to the folid X. make the fame conftruction as in the preceeding Propofition , and it may be demonftrated the very fame way as in that Propofition , that the pyramid of which the base ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
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 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 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.
Σελίδα 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.