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 79.
Σελίδα 190
... folid figure contained by fix equal fquares . XXVI . A Tetrahedron is a folid figure contained by four equal and equila- teral triangles . XXVII . An Octahedron is a folid figure contained by eight equal and equi- lateral triangles ...
... folid figure contained by fix equal fquares . XXVI . A Tetrahedron is a folid figure contained by four equal and equila- teral triangles . XXVII . An Octahedron is a folid figure contained by eight equal and equi- lateral triangles ...
Σελίδα 205
... folid angle at A be contained by the three plane angles BAC , CAD , DAB . any two of them are greater than the third ... folid angle , & c . QE . D. PROP . XXI . THEOR . EVERY folid angle is contained by plane angles which ' together are ...
... folid angle at A be contained by the three plane angles BAC , CAD , DAB . any two of them are greater than the third ... folid angle , & c . QE . D. PROP . XXI . THEOR . EVERY folid angle is contained by plane angles which ' together are ...
Σελίδα 206
... folid angle at A , are less than four right angles . Next , Let the folid angle at A be contained by any number of plane angles BAC , CAD , DAE , EAF , FAB ; thefe together are lefs than four right angles . Let the planes in which the ...
... folid angle at A , are less than four right angles . Next , Let the folid angle at A be contained by any number of plane angles BAC , CAD , DAE , EAF , FAB ; thefe together are lefs than four right angles . Let the planes in which the ...
Σελίδα 207
... folid angle at A , are less than four right angles . Therefore every folid angle , & c . Q. E. D. 32. I. PROP . XXII . THEOR . IF every two of three plane angles be greater than the see N. third , and if the straight lines which contain ...
... folid angle at A , are less than four right angles . Therefore every folid angle , & c . Q. E. D. 32. I. PROP . XXII . THEOR . IF every two of three plane angles be greater than the see N. third , and if the straight lines which contain ...
Σελίδα 208
... folid angle which fhall be contained by three given plane angles , any two of them being greater than the third , and all three together less than four right angles . Let the three given plane angles be ABC , DEF , GHK , any two of ...
... folid angle which fhall be contained by three given plane angles , any two of them being greater than the third , and all three together less than four right angles . Let the three given plane angles be ABC , DEF , GHK , any two of ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.