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 18
Seite 189
... and which are contained by the same number of similar planes . XII . A Pyramid is a solid figure contained by planes that are constituted betwixt one plane and one point above it in which they meet . XIII . A Prism is a solid figure ...
... and which are contained by the same number of similar planes . XII . A Pyramid is a solid figure contained by planes that are constituted betwixt one plane and one point above it in which they meet . XIII . A Prism is a solid figure ...
Seite 221
A E one BE ; and the parallelogram GE to CH : therefore the prism contained by the two triangles CGF , DAE , and the three parallelograms CA , GE , EC , is equal e to the e . C. 11 . prism contained by the two triangles CBF , DHE , and ...
A E one BE ; and the parallelogram GE to CH : therefore the prism contained by the two triangles CGF , DAE , and the three parallelograms CA , GE , EC , is equal e to the e . C. 11 . prism contained by the two triangles CBF , DHE , and ...
Seite 222
11. opposite planes ALGF , CBHD , AH is cut into two equal parts by the plane AGHC . therefore the D H K folid AH is double of the prism which is contained by the triF G angles ALG , CBH . for the same reason , because the folid C B AK ...
11. opposite planes ALGF , CBHD , AH is cut into two equal parts by the plane AGHC . therefore the D H K folid AH is double of the prism which is contained by the triF G angles ALG , CBH . for the same reason , because the folid C B AK ...
Seite 223
from the solid of which the base is the parallelogram AB , and in Book XI . which FDKN is the one opposite to it ; and if from this fame folid there be taken the prism AFG , CDE ; the remaining folid , viz . the parallelepiped AH ...
from the solid of which the base is the parallelogram AB , and in Book XI . which FDKN is the one opposite to it ; and if from this fame folid there be taken the prism AFG , CDE ; the remaining folid , viz . the parallelepiped AH ...
Seite 227
Let the prisms the bases of which are the triangles ALM , CFO , and NBO , PDQ the triangles opposite to them , have the same altitude ; and complete the parallelograms AE , CF , and the solid parallclepipeds AB , CD , in the firit of ...
Let the prisms the bases of which are the triangles ALM , CFO , and NBO , PDQ the triangles opposite to them , have the same altitude ; and complete the parallelograms AE , CF , and the solid parallclepipeds AB , CD , in the firit of ...
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 |