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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Σελίδα 9
... base BC shall coincide with the base EF because the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impoffible . There- a . 10. Ax . fore the ...
... base BC shall coincide with the base EF because the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impoffible . There- a . 10. Ax . fore the ...
Σελίδα 10
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal fides are opposite ; viz . the angle ACF ...
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal fides are opposite ; viz . the angle ACF ...
Σελίδα 11
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the B less to the greater ; which is abfurd . There- Cb . 4. 1 . fore AB is not unequal to AC , that is , it is equal to it . Wherefore if two angles ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the B less to the greater ; which is abfurd . There- Cb . 4. 1 . fore AB is not unequal to AC , that is , it is equal to it . Wherefore if two angles ...
Σελίδα 12
... base CD are equal one another ; but the angle ECD is great- C 2 to er than the angle BCD , wherefore the angle FDC ... base , and on the same side of it , there cannot be two triangles that have their fides which are terminated in ...
... base CD are equal one another ; but the angle ECD is great- C 2 to er than the angle BCD , wherefore the angle FDC ... base , and on the same side of it , there cannot be two triangles that have their fides which are terminated in ...
Σελίδα 13
... base BC coincides with the base EF , but the fides BA , CA do not coincide with the fides ED , FD , but have a different situation , as EG , FG ; then upon the same base EF and upon the fame side of it there can be two triangles that ...
... base BC coincides with the base EF , but the fides BA , CA do not coincide with the fides ED , FD , but have a different situation , as EG , FG ; then upon the same base EF and upon the fame side of it there can be two triangles that ...
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio biſected Book XI cafe cauſe circle ABCD circumference cone conſtruction cylinder demonftrated deſcribed diameter drawn equal angles equiangular equimultiples Euclid exceſs fame multiple fame ratio fame reaſon fides fimilar firſt folid angle fore given angle given in magnitude given in poſition given in ſpecies given magnitude given ratio given ſtraight line gnomon greater join leſs Let ABC likewife oppoſite parallel parallelepipeds parallelogram perpendicular priſms Propofition proportionals pyramid Q. E. D. PROP rectangle rectangle contained rectilineal figure right angles ſame ſecond ſegment ſhall ſhewn ſide ſpace ſphere ſquare of AC ſtraight line AB ſtraight line BC THEOR theſe thoſe tiple triangle ABC vertex 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.