The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood1856 |
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Seite 57
... drawn from A to D B equal to A C. Cor . 1. - If a straight line be shorter than any other that can be drawn from a point without a straight line to that line , the former straight line is perpendicular to the latter . Cor . 2. - The ...
... drawn from A to D B equal to A C. Cor . 1. - If a straight line be shorter than any other that can be drawn from a point without a straight line to that line , the former straight line is perpendicular to the latter . Cor . 2. - The ...
Seite 59
... drawn from C to AB equal to CA ( Prop . 26 ) , no other point in A B coincides with any point in the circle ; or , in other words , the straight line AB cuts the circle in no other point . XXIX . The perpendicular at the extremity of a ...
... drawn from C to AB equal to CA ( Prop . 26 ) , no other point in A B coincides with any point in the circle ; or , in other words , the straight line AB cuts the circle in no other point . XXIX . The perpendicular at the extremity of a ...
Seite 60
... drawn between that and the circle so as not to cut the circle . Let A B ( Fig . 21 ) be the diameter of a circle ; C , the centre ; BE perpendicular to BC . BE will fall wholly without the circle , and no straight line can be drawn ...
... drawn between that and the circle so as not to cut the circle . Let A B ( Fig . 21 ) be the diameter of a circle ; C , the centre ; BE perpendicular to BC . BE will fall wholly without the circle , and no straight line can be drawn ...
Seite 61
... drawn from it to the circumference the greatest is that in which the centre is , and the other part of the diameter is the least ; and of any others , that which makes a less angle with the line which passes through the centre is ...
... drawn from it to the circumference the greatest is that in which the centre is , and the other part of the diameter is the least ; and of any others , that which makes a less angle with the line which passes through the centre is ...
Seite 62
... drawn two equal lines from F to the circumference , one upon each side of the shortest line FD . At the point E let the line EF make the angle FE H equal to the angle CEF and join FH . Then because CE is equal to E H , and FE is common ...
... drawn two equal lines from F to the circumference , one upon each side of the shortest line FD . At the point E let the line EF make the angle FE H equal to the angle CEF and join FH . Then because CE is equal to E H , and FE is common ...
Andere Ausgaben - Alle anzeigen
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The Geometry of the Three First Books of Euclid, by Direct Proof From ... Euclid,Hensleigh Wedgwood Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
A B C D angle A B C angle ABC angle B A C angle BAC AUGUSTUS DE MORGAN axiom of Euclid B C is equal base B C bisected centre Chap coincide conception cuts the circle D E F definition diameter DIONYSIUS LARDNER Electric Telegraph equal to twice ex absurdo exterior angle F. W. NEWMAN Fcap geometry Greek less London magnitude motion opposite angles parallel straight lines parallelogram perpendicular plane surface position price 5d Professor Prop proportion proposition rectangle A C rectangle A D rectangle contained relation right angles segment sides A B squares of A C straight line joining tion touching the circle track transverse triangle A B C twice the rectangle University College Vols wherefore 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...