The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood1856 |
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Side 2
... greater than either of the others , without , in the first place , considering whether the angles will be equal or unequal , or which of them will be the greater ; but geometry teaches us , that if two sides of a triangle are equal ...
... greater than either of the others , without , in the first place , considering whether the angles will be equal or unequal , or which of them will be the greater ; but geometry teaches us , that if two sides of a triangle are equal ...
Side 12
... greater or less than the distance simulta- neously traversed in the other . An agent carried along in a certain direction by the motion of the rigid system in which he is placed , as in the cabin of a ship for instance , has the same ...
... greater or less than the distance simulta- neously traversed in the other . An agent carried along in a certain direction by the motion of the rigid system in which he is placed , as in the cabin of a ship for instance , has the same ...
Side 21
... Greater , and Less , are laid down in the nine first axioms of Euclid , the whole of which may conveniently be replaced by a single proposition enouncing the conditions by which the equality of given dimensions , or the superior ...
... Greater , and Less , are laid down in the nine first axioms of Euclid , the whole of which may conveniently be replaced by a single proposition enouncing the conditions by which the equality of given dimensions , or the superior ...
Side 22
... greater and less , is identity or excess , on one side or the other , in respect of the quantity of space occupied by the dimensions compared ; and thus the relative mag- nitude of particular dimensions must ultimately be tried by ...
... greater and less , is identity or excess , on one side or the other , in respect of the quantity of space occupied by the dimensions compared ; and thus the relative mag- nitude of particular dimensions must ultimately be tried by ...
Side 23
... greater , the included the less . The process by which it is shewn that one figure may be applied to , or made to coincide with , another , for the purpose of ascertaining their rela- tive magnitude , is called the proof by ...
... greater , the included the less . The process by which it is shewn that one figure may be applied to , or made to coincide with , another , for the purpose of ascertaining their rela- tive magnitude , is called the proof by ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 26 - If two triangles have two sides of the one equal to two sides of the...