Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey |
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Page 2
... Similarly , because D is the centre of the circle GKL , therefore DG = DL . But in the lines DG and DL we have DB = DA ( cons . ) , therefore BG = AL ( ax . 3 ) . Also it has been shown that BG = BC ; therefore AL = BC ( ax . 1 ) ...
... Similarly , because D is the centre of the circle GKL , therefore DG = DL . But in the lines DG and DL we have DB = DA ( cons . ) , therefore BG = AL ( ax . 3 ) . Also it has been shown that BG = BC ; therefore AL = BC ( ax . 1 ) ...
Page 1
... Similarly , because B is the centre of the circle ACE , therefore BA = BC . But it has been proved that BA = AC , therefore AC = BC ( ax . 1 ) , and therefore AB , BC , and CA each other . Therefore , it is proved , as required , that ...
... Similarly , because B is the centre of the circle ACE , therefore BA = BC . But it has been proved that BA = AC , therefore AC = BC ( ax . 1 ) , and therefore AB , BC , and CA each other . Therefore , it is proved , as required , that ...
Page 2
... Similarly , because D is the centre of the circle GKL , therefore DG = DL . But in the lines DG and DL we have DB = DA ( cons . ) , therefore BG = AL ( ax . 3 ) . Also it has been shown that BG = BC ; therefore AL = BC ( ax . 1 ) ...
... Similarly , because D is the centre of the circle GKL , therefore DG = DL . But in the lines DG and DL we have DB = DA ( cons . ) , therefore BG = AL ( ax . 3 ) . Also it has been shown that BG = BC ; therefore AL = BC ( ax . 1 ) ...
Page 8
... supposition that AB is greater than AC is absurd . Similarly the supposition that AB is less than AC might be shown to be absurd . Therefore , it is proved , as required , that 8 EUCLID , BOOK I. Then it is to be proved that ...
... supposition that AB is greater than AC is absurd . Similarly the supposition that AB is less than AC might be shown to be absurd . Therefore , it is proved , as required , that 8 EUCLID , BOOK I. Then it is to be proved that ...
Page 13
... Similarly , 2. The angle ABC the angle DEF . 3. The angle ACB the angle DFE . Wherefore , If two triangles , & c . Q. E. D. N.B. - The equality of the two triangles , in every respect , follows from this Proposition , as it does from ...
... Similarly , 2. The angle ABC the angle DEF . 3. The angle ACB the angle DFE . Wherefore , If two triangles , & c . Q. E. D. N.B. - The equality of the two triangles , in every respect , follows from this Proposition , as it does from ...
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Common terms and phrases
ABCD AC and CD alternate angle angle ABC angle ACB angle AGH angle BAC Arithmetic base BC Beginners bisected Book centre circle coincides cons Construction CONSTRUCTION.-1 crown 8vo describe Dictionary divided double the square draw drawn Edition Elementary English equal Euclid Exercises exterior angle falls figure former four French Geography German given straight line gnomon greater Greek half History join Language Latin latter less Lessons Let ABC London LONGMANS Manual Maps meet Notes opposite angle parallel parallelogram Plane post 8vo PROBLEM produced proof PROOF.-Because PROP Proposition proved Reader Reading rect rectangle contained rectilineal right angles School Second side AC Similarly small 8vo square on AC Standard Stepping-Stone straight line supposition THEOREM third translated triangle ABC vols Wherefore whole
Popular passages
Page 48 - 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 equal to two right angles.
Page 88 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 14 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 64 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Page 108 - In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B an acute angle; and on BC one of the sides containing it, let fall the perpendicular...
Page 47 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Page 104 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 52 - The straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Page 20 - If, at a point in a straight line, two other straight lines upon the opposite sides of it, make the adjacent angles, together equal to two right angles, these two straight lines shall be in one and the same straight line.