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 sider |
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Side 115
... magnitude of which a multiple is greater than the fame mul- tiple of another , is greater than that other magnitude . PROP . I. THEOR . IF F any number of magnitudes be equimultiples of as many , each of each ; what multiple foever any ...
... magnitude of which a multiple is greater than the fame mul- tiple of another , is greater than that other magnitude . PROP . I. THEOR . IF F any number of magnitudes be equimultiples of as many , each of each ; what multiple foever any ...
Side 116
... magnitude be the fame multiple of the fecond that the third is of the fourth , and the fifth the fame multiple of ... magnitudes in AB equal to C , as there are in DE equal to F. in like manner , as many as there are in BG equal to C , G ...
... magnitude be the fame multiple of the fecond that the third is of the fourth , and the fifth the fame multiple of ... magnitudes in AB equal to C , as there are in DE equal to F. in like manner , as many as there are in BG equal to C , G ...
Side 119
... magnitude be the fame multiple of another , See N. which a magnitude taken from the first is of a magni- tude taken from the other ; the remainder fhall be the fame multiple of the remainder , that the whole is of the whole . Let the ...
... magnitude be the fame multiple of another , See N. which a magnitude taken from the first is of a magni- tude taken from the other ; the remainder fhall be the fame multiple of the remainder , that the whole is of the whole . Let the ...
Side 120
... magnitude , & c . Q. E. D. See N. IF PROP . VI . THEOR . two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to thefe others , or equi- multiples of ...
... magnitude , & c . Q. E. D. See N. IF PROP . VI . THEOR . two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to thefe others , or equi- multiples of ...
Side 121
... magnitudes are proportionals , they are propor- See N. tionals alfo when taken inverfely . If the magnitude A be to B , as C is to D , then alfo inversely B is to A , as D to C. Take of B and D any equimultiples what- ever E and F ; and ...
... magnitudes are proportionals , they are propor- See N. tionals alfo when taken inverfely . If the magnitude A be to B , as C is to D , then alfo inversely B is to A , as D to C. Take of B and D any equimultiples what- ever E and F ; and ...
Andre utgaver - Vis alle
The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Side 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.
Side 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.
Side 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.