The geometry of the three first books of Euclid, by direct proof from definitions alone, by H. Wedgwood1856 |
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Page 2
... 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 , the angles opposite to the equal sides are also equal to each other ; and if the sides are ...
... 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 , the angles opposite to the equal sides are also equal to each other ; and if the sides are ...
Page 35
... opposite sides are parallel to each other . When the angles are all right angles the paral- lelogram becomes a rectangle ; and when all the sides are equal the figure is a square . XIII . - EQUAL , GREATER , LESS . Magnitudes ...
... opposite sides are parallel to each other . When the angles are all right angles the paral- lelogram becomes a rectangle ; and when all the sides are equal the figure is a square . XIII . - EQUAL , GREATER , LESS . Magnitudes ...
Page 39
... opposite to AB , and is therefore in the same direction with AC , and B A C forms a single straight line . V. All right angles are equal . Let BAC , EDF , be any two right angles ( fig . 2 ) , and let BA and ED be produced to G and H ...
... opposite to AB , and is therefore in the same direction with AC , and B A C forms a single straight line . V. All right angles are equal . Let BAC , EDF , be any two right angles ( fig . 2 ) , and let BA and ED be produced to G and H ...
Page 41
... opposite angles , made by two straight lines cutting each other , are equal to each other . Let the two straight lines A B , CD ( Fig . 4 ) , cut one another in the point E , the angle A E C shall be equal to the angle DE B , and CEB to ...
... opposite angles , made by two straight lines cutting each other , are equal to each other . Let the two straight lines A B , CD ( Fig . 4 ) , cut one another in the point E , the angle A E C shall be equal to the angle DE B , and CEB to ...
Page 47
... opposite angle A B C. Therefore the whole angle A CD , consisting of the two angles A CE , ECD , is equal to the two in- terior and opposite angles A B C , BA C. To each of these add the angle AC B. Then the three interior angles of the ...
... opposite angle A B C. Therefore the whole angle A CD , consisting of the two angles A CE , ECD , is equal to the two in- terior and opposite angles A B C , BA C. To each of these add the angle AC B. Then the three interior angles of the ...
Other editions - View all
The Geometry of the Three First Books of Euclid, by Direct Proof from ... Euclid No preview available - 2012 |
The Geometry of the Three First Books of Euclid, by Direct Proof from ... Euclid,Hensleigh Wedgwood No preview available - 2015 |
The Geometry of the Three First Books of Euclid, by Direct Proof From ... Euclid,Hensleigh Wedgwood No preview available - 2018 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 26 - If two triangles have two sides of the one equal to two sides of the...