The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood |
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Seite 41
... are together equal to two right angles ; and the angles C EB , BED , on one side of the straight line C D , are also equal to two right angles ; wherefore the angles A EC , CEB , are together equal to the two CEB , BED .
... are together equal to two right angles ; and the angles C EB , BED , on one side of the straight line C D , are also equal to two right angles ; wherefore the angles A EC , CEB , are together equal to the two CEB , BED .
Seite 45
Wherefore ( Prop . 9 ) the angle CAB is equal to GCD . Next , let AB , CD , be straight lines in the same plane , making the angle CAB equal to GCD ; C D shall be parallel to A B. Because AC is in the same direction with CG , and the ...
Wherefore ( Prop . 9 ) the angle CAB is equal to GCD . Next , let AB , CD , be straight lines in the same plane , making the angle CAB equal to GCD ; C D shall be parallel to A B. Because AC is in the same direction with CG , and the ...
Seite 56
... and AE is the only line that can be drawn from À to D B equal to A C. Because the angle ABC is a right angle , the angle A CB is less than a right angle ; wherefore the side A C is greater than A B , 56 PROPOSITIONS .
... and AE is the only line that can be drawn from À to D B equal to A C. Because the angle ABC is a right angle , the angle A CB is less than a right angle ; wherefore the side A C is greater than A B , 56 PROPOSITIONS .
Seite 57
Therefore the triangles ABC , A B E are equal , and the side A E is equal to A C , and every other line on the other side of B from C is ( by the present Prop . ) either greater than A E or less ; wherefore A E is the only line that can ...
Therefore the triangles ABC , A B E are equal , and the side A E is equal to A C , and every other line on the other side of B from C is ( by the present Prop . ) either greater than A E or less ; wherefore A E is the only line that can ...
Seite 58
... is equal to A E and EF , that is , to E B and EF . But E B and EF are together greater than FB , the third side of the triangle E B F ; therefore AF is greater than F B. Wherefore F is not the centre of the circle , 58 PROPOSITIONS .
... is equal to A E and EF , that is , to E B and EF . But E B and EF are together greater than FB , the third side of the triangle E B F ; therefore AF is greater than F B. Wherefore F is not the centre of the circle , 58 PROPOSITIONS .
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The Geometry of the Three First Books of Euclid, by Direct Proof from ... Euclid Keine Leseprobe verfügbar - 2012 |
The Geometry of the Three First Books of Euclid, by Direct Proof From ... Euclid,Hensleigh Wedgwood Keine Leseprobe verfügbar - 2018 |
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 |