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 1 - 5 από τα 100.
Σελίδα 5
... Parallel ftraight lines , are fuch as are in the fame plane , and which being produced ever fo far both ways , do not meet . POSTULATE S. I , ET it be granted that a straight line may be drawn from any one point to any other point . LE ...
... Parallel ftraight lines , are fuch as are in the fame plane , and which being produced ever fo far both ways , do not meet . POSTULATE S. I , ET it be granted that a straight line may be drawn from any one point to any other point . LE ...
Σελίδα 26
... parallel . Let the straight line EF which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For if it be not parallel , AB and CD being produced shall meet ei ...
... parallel . Let the straight line EF which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . For if it be not parallel , AB and CD being produced shall meet ei ...
Σελίδα 28
... parallel to the fame straight line , are parallel to one another . Let AB , CD be each of them parallel to EF ; AB is alfo parallel to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight lines AB ...
... parallel to the fame straight line , are parallel to one another . Let AB , CD be each of them parallel to EF ; AB is alfo parallel to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight lines AB ...
Σελίδα 29
... parallel to the given straight line BC . Book I. Which was to be done . PROP . XXXII . THEOR . IF a fide of any ... parallel to the straight line AB . and a . 31. I. because AB is parallel to CE , and AC meets them , the al- ternate ...
... parallel to the given straight line BC . Book I. Which was to be done . PROP . XXXII . THEOR . IF a fide of any ... parallel to the straight line AB . and a . 31. I. because AB is parallel to CE , and AC meets them , the al- ternate ...
Σελίδα 30
... parallel . Let AB , CD be equal and parallel straight lines , and joined to- wards the fame parts by the straight A lines AC , BD ; AC , BD are alfo equal and parallel . Join BC , and because AB is pa- rallel to CD , and BC meets them ...
... parallel . Let AB , CD be equal and parallel straight lines , and joined to- wards the fame parts by the straight A lines AC , BD ; AC , BD are alfo equal and parallel . Join BC , and because AB is pa- rallel to CD , and BC meets them ...
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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.