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
... fourth , when any 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 ...
... fourth , when any 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 ...
Seite 112
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by faying , the firft is to the fecond , as the third to ' the fourth . ' VII . When of ...
... fourth . VI . Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ufually expreffed by faying , the firft is to the fecond , as the third to ' the fourth . ' VII . When of ...
Seite 113
... fourth ; or that the first is to the third , as the fecond to the fourth . as is fhewn in the 16th Prop . of this 5th Book . XIV . Invertendo , by Inverfion ; when there are four proportionals , and it is inferred , that the fecond is ...
... fourth ; or that the first is to the third , as the fecond to the fourth . as is fhewn in the 16th Prop . of this 5th Book . XIV . Invertendo , by Inverfion ; when there are four proportionals , and it is inferred , that the fecond is ...
Seite 114
... fourth of the firft rank , fo is the third from the laft to the last but two of the fecond rank ; and fo on in a crofs order . and the inference is as in the 18th Definition . It is demonftrated in 23d Prop . of Book 5th . E AXIOM S. I. ...
... fourth of the firft rank , fo is the third from the laft to the last but two of the fecond rank ; and fo on in a crofs order . and the inference is as in the 18th Definition . It is demonftrated in 23d Prop . of Book 5th . E AXIOM S. I. ...
Seite 116
... fourth , and the fifth the fame multiple of the second that the fixth is of the fourth ; then fhall the first together with the fifth be the fame multiple of the fecond , that the third together with the fixth is of the fourth . Then is ...
... fourth , and the fifth the fame multiple of the second that the fixth is of the fourth ; then fhall the first together with the fifth be the fame multiple of the fecond , that the third together with the fixth is of the fourth . Then is ...
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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 |