The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
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Seite 172
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 contained by plane figures , of which two that are opposite are equal ...
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 contained by plane figures , of which two that are opposite are equal ...
Seite 226
D Let there be a pyramid of which the base is the triangle ABC and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids having triangular bases , and similar to the whole ; and into two equal ...
D Let there be a pyramid of which the base is the triangle ABC and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids having triangular bases , and similar to the whole ; and into two equal ...
Seite 227
Therefore the pyramid , of which the base is the triangle AEG , and of which the vertex is the point H , is equal * and similar to the pyramid , the * C. 11 . base of which is the triangle KHL , and vertex the point D. And because HK is ...
Therefore the pyramid , of which the base is the triangle AEG , and of which the vertex is the point H , is equal * and similar to the pyramid , the * C. 11 . base of which is the triangle KHL , and vertex the point D. And because HK is ...
Seite 228
of which the base is the triangle AEG , and vertex H : therefore each of the pyramids AEGH , HKLD is similar to the whole pyramid ABCD . And because BF is equal to FC , the parallelogram EBFG is double * of the triangle GFC : but when ...
of which the base is the triangle AEG , and vertex H : therefore each of the pyramids AEGH , HKLD is similar to the whole pyramid ABCD . And because BF is equal to FC , the parallelogram EBFG is double * of the triangle GFC : but when ...
Seite 229
THEOR . . ; If there be two pyramids of the same altitude , upon tri . See N. angular bases , and each of them be divided into two equal pyramids similar to the rohole pyramid , and also into two equal prisms ; and if each of these ...
THEOR . . ; If there be two pyramids of the same altitude , upon tri . See N. angular bases , and each of them be divided into two equal pyramids similar to the rohole pyramid , and also into two equal prisms ; and if each of these ...
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added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole
Beliebte Passagen
Seite 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Seite 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.
Seite 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Seite 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...
Seite 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.
Seite 97 - 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.
Bibliografische Informationen
| Titel | The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |
| Autor/in | Robert Simson |
| Herausgeber | Richard Newton Adams |
| Übersetzt von | Abram Robertson |
| Verlag | J. Collingwood, 1827 |
| Original von | University of Michigan |
| Digitalisiert | 11. Juni 2007 |
| Länge | 513 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |