The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood1856 |
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Seite 34
... passing through each successive point that can be reached from a given point by motion in a single constant direction . VIII . - PARALLEL STRAIGHT LINES . Parallel straight lines are straight lines lying in the same direction in a ...
... passing through each successive point that can be reached from a given point by motion in a single constant direction . VIII . - PARALLEL STRAIGHT LINES . Parallel straight lines are straight lines lying in the same direction in a ...
Seite 35
... passing through every point in a plane which lies at a certain given distance from a point called the centre of the circle . A straight line from the centre to the circum- ference is called the radius . XI . TRIANGLE . A triangle is a ...
... passing through every point in a plane which lies at a certain given distance from a point called the centre of the circle . A straight line from the centre to the circum- ference is called the radius . XI . TRIANGLE . A triangle is a ...
Seite 62
... greatest is that which passes through the cen- tre , and of the rest , that which makes a less angle with the line passing through the centre is greater than that which makes a greater angle with it . 62 PROPOSITIONS .
... greatest is that which passes through the cen- tre , and of the rest , that which makes a less angle with the line passing through the centre is greater than that which makes a greater angle with it . 62 PROPOSITIONS .
Seite 67
... passing through the centre ( Prop . 32 ) of the latter circle is greater than the line passing through the centre . Therefore DA cannot be one of the lines from D to the circle C not passing through the centre C , that is , it does does ...
... passing through the centre ( Prop . 32 ) of the latter circle is greater than the line passing through the centre . Therefore DA cannot be one of the lines from D to the circle C not passing through the centre C , that is , it does does ...
Seite 68
... . 26 ) . Then , because C is a point without the circle B , and C K a line passing through the centre , and CD and C E equi- distant on either side of C K ( Prop . 30 ) , every line from C to circle B , between CD and CE 68 PROPOSITIONS .
... . 26 ) . Then , because C is a point without the circle B , and C K a line passing through the centre , and CD and C E equi- distant on either side of C K ( Prop . 30 ) , every line from C to circle B , between CD and CE 68 PROPOSITIONS .
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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...