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 Seiten |
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Seite 111
... equimultiples whatsoever of the firft and third being taken , and any equimul- tiples whatsoever of the fecond and fourth ; if the multiple of the first be less than that of the fecond , the multiple of the third is álfo less than that ...
... equimultiples whatsoever of the firft and third being taken , and any equimul- tiples whatsoever of the fecond and fourth ; if the multiple of the first be less than that of the fecond , the multiple of the third is álfo less than that ...
Seite 112
... equimultiples of four magnitudes ( taken as in the 5th Definition ) the multiple of the first is greater than that of the fe- cond , but the multiple of the third is not greater than the mul- tiple of the fourth ; then the firft is faid ...
... equimultiples of four magnitudes ( taken as in the 5th Definition ) the multiple of the first is greater than that of the fe- cond , but the multiple of the third is not greater than the mul- tiple of the fourth ; then the firft is faid ...
Seite 114
... equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the fame multiple of a lefs . 4. Prop . Lib . 2. Archimedis de fphaera et cylindro . IV . That IV . That magnitude of which a multiple is ...
... equimultiples , are equal to one another . III . A multiple of a greater magnitude is greater than the fame multiple of a lefs . 4. Prop . Lib . 2. Archimedis de fphaera et cylindro . IV . That IV . That magnitude of which a multiple is ...
Seite 115
... equimultiples of as many , each of each ; what multiple foever any one of them is of its part , the fame multiple fhall all the first magnitudes be of all the other . El Let any number of magnitudes AB , CD be equimultiples of as many ...
... equimultiples of as many , each of each ; what multiple foever any one of them is of its part , the fame multiple fhall all the first magnitudes be of all the other . El Let any number of magnitudes AB , CD be equimultiples of as many ...
Seite 117
... equimultiples , these shall be equimultiples the one of the fecond , and the other of the fourth . Let A the first be the fame multiple of B the fecond , that C the third is of D the fourth ; and of A , C let the equimultiples EF , GH ...
... equimultiples , these shall be equimultiples the one of the fecond , and the other of the fourth . Let A the first be the fame multiple of B the fecond , that C the third is of D the fourth ; and of A , C let the equimultiples EF , GH ...
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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
Beliebte Passagen
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Seite 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.
Seite 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.
Seite 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.
Bibliografische Informationen
| Titel | 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 ... |
| Autor/in | Robert Simson |
| Verlag | R. and A. Foulis, 1762 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 466 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |