The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood |
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Seite 22
... may be applied to each other , so as wholly to coincide or occupy the same space , or to coincide to the whole extent of one of the magnitudes , leaving a portion of the other unoccupied . The result in 22 INTRODUCTION .
... may be applied to each other , so as wholly to coincide or occupy the same space , or to coincide to the whole extent of one of the magnitudes , leaving a portion of the other unoccupied . The result in 22 INTRODUCTION .
Seite 23
The result in the former case , will be to shew that dimensions of the kind in question are necessarily equal to each other ; in the latter , that the dimension which wholly coincides with a part of the other , is the less of the two .
The result in the former case , will be to shew that dimensions of the kind in question are necessarily equal to each other ; in the latter , that the dimension which wholly coincides with a part of the other , is the less of the two .
Seite 24
... that figures constructed according to a certain plan , when properly applied to each other , must necessarily either wholly coincide , or partially coincide , leaving a clear excess on the one side or the other .
... that figures constructed according to a certain plan , when properly applied to each other , must necessarily either wholly coincide , or partially coincide , leaving a clear excess on the one side or the other .
Seite 34
Points in the same position are said to coincide . Lines , surfaces , and solids coincide respectively when every point in each of the magnitudes compared coincides with a corresponding point in the other . VII . - STRAIGHT LINE .
Points in the same position are said to coincide . Lines , surfaces , and solids coincide respectively when every point in each of the magnitudes compared coincides with a corresponding point in the other . VII . - STRAIGHT LINE .
Seite 36
EQUAL , GREATER , LESS . one may Magnitudes are equal to each other when the one may be made exactly to coincide with the other , or when they may be divided into a number of parts , so that the sum of all the parts of the be made to ...
EQUAL , GREATER , LESS . one may Magnitudes are equal to each other when the one may be made exactly to coincide with the other , or when they may be divided into a number of parts , so that the sum of all the parts of the be made to ...
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Häufige Begriffe und Wortgruppen
analysis attained Author base Book centre Chap circle circumference cloth coincide common conception construction cutting definition diameter direction distance divided double drawn Edition elements English equal Euclid expressed fall figure fundamental geometry given greater Greek Illustrations Join known less lettered London magnitude meet motion moving necessary numerous object opposite originally parallel parallelogram passing perpendicular plane position possible Principles produced Professor proof Prop proportion proposition reason rectangle contained relation remaining respectively right angles School segment side space square square of BC straight line student surface third tion touch track transverse triangle triangle A B C twice the rectangle University College Vols Volume wherefore whole wholly
Beliebte Passagen
Seite 62 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Seite 64 - IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Seite 98 - Museum of Science and Art. THE MUSEUM OF SCIENCE AND ART. Edited by DIONYSIUS LARDNER, DCL, formerly Professor of Natural Philosophy and Astronomy in University College, London. With upwards of 1 200 Engravings on Wood.
Seite 80 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Seite 25 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 78 - BAC is cut off from the given circle ABC containing an angle equal to the given angle D : Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other.
Seite 97 - This is quite a novelty in chronological literature. It is an universal almanac — universal, that is, as respects time, past, present, and future. The main object of it is, as the compiler states, to supply the place of an old almanac, which is never at hand when wanted ; of the older almanac, which never was at hand ; and of the universal almanac in every shape IA more useful chronological handbook could scarcely be conceived.
Seite 24 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Seite 26 - If two triangles have two sides of the one equal to two sides of the...
Bibliografische Informationen
| Titel | The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood |
| Autor/in | Euclides |
| Herausgeber | Hensleigh Wedgwood |
| Veröffentlicht | 1856 |
| Original von | Oxford University |
| Digitalisiert | 8. Sept. 2006 |
| Zitat exportieren | BiBTeX EndNote RefMan |