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 twelfth |
Im Buch
Ergebnisse 1-5 von 51
Seite 111
Magnitudes are said to have a ratio to one another , when the less can be multiplied fo as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when ...
Magnitudes are said to have a ratio to one another , when the less can be multiplied fo as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , when ...
Seite 112
Book V. than that of the second , the multiple of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals . N. B. · When four magnitudes are proportionals , it is usually ...
Book V. than that of the second , the multiple of the third is also greater than that of the fourth . VI . Magnitudes which have the same ratio are called proportionals . N. B. · When four magnitudes are proportionals , it is usually ...
Seite 113
See it . word is used when there are four proportionals , and it is infer red , that the first has the same ratio to the third , which the fecond has to the fourth ; or that the first is to the third , as the fecond to the fourth . as ...
See it . word is used when there are four proportionals , and it is infer red , that the first has the same ratio to the third , which the fecond has to the fourth ; or that the first is to the third , as the fecond to the fourth . as ...
Seite 114
... is to the fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order . and the inference is as in the 18th Definition . It is demonstrated in 23d Prop . of Book 5th .
... is to the fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order . and the inference is as in the 18th Definition . It is demonstrated in 23d Prop . of Book 5th .
Seite 116
If F the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the fixth is of the fourth ; then Thall the first together with the fifth be the same ...
If F the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the fixth is of the fourth ; then Thall the first together with the fifth be the same ...
Was andere dazu sagen - Rezension schreiben
Es wurden keine Rezensionen gefunden.
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book caſe circle circle ABCD circumference common cone contained cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides firſt folid fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe magnitude manner meet muſt oppoſite parallel parallelogram perpendicular plane priſm produced PROP proportionals Propoſition pyramid reaſon rectangle remaining right angles ſame ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſquare ſquare of BC taken THEOR theſe third thro triangle ABC wherefore whole
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 |