Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey |
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Page xx
... Parallelograms , as this definition shows . For the terms Rhombus and Rhomboid that of Parallelogram is often used ; and for Oblong the term Rectangle . 35 . PARALLEL STRAIGHT LINES are such as are in the same plane , and which , being ...
... Parallelograms , as this definition shows . For the terms Rhombus and Rhomboid that of Parallelogram is often used ; and for Oblong the term Rectangle . 35 . PARALLEL STRAIGHT LINES are such as are in the same plane , and which , being ...
Page 56
... parallelogram are equal to one another , and the diameter bisects the parallelogram , that is , divides it into two equal parts . Let ABDC be a parallelogram , of which BC is a diameter . Then it is to be proved that 1. The opposite ...
... parallelogram are equal to one another , and the diameter bisects the parallelogram , that is , divides it into two equal parts . Let ABDC be a parallelogram , of which BC is a diameter . Then it is to be proved that 1. The opposite ...
Page 57
... parallelogram are equal to one another . 2. Next , because in the triangles ABC and BCD we have the sides AB and BC , and their angle ABC , in the former the sides DC and CB , and their angle DCB , in the latter , each to each , as here ...
... parallelogram are equal to one another . 2. Next , because in the triangles ABC and BCD we have the sides AB and BC , and their angle ABC , in the former the sides DC and CB , and their angle DCB , in the latter , each to each , as here ...
Page 58
... parallelograms on the same base BC , and between the same parallels AF and BC . Then it is to be proved that The parallelogram ABCD = the parallelogram EBCF . This Proposition is considered under three Cases . CASE I. In this Case the ...
... parallelograms on the same base BC , and between the same parallels AF and BC . Then it is to be proved that The parallelogram ABCD = the parallelogram EBCF . This Proposition is considered under three Cases . CASE I. In this Case the ...
Page 59
... parallelogram EBCF ; and if we take the triangle FDC from the same trapezium FABC , we have left the parallelogram DABC ; and these remainders are equal ( ax . 3 ) . Therefore , it is proved in this Case , as required , that The ...
... parallelogram EBCF ; and if we take the triangle FDC from the same trapezium FABC , we have left the parallelogram DABC ; and these remainders are equal ( ax . 3 ) . Therefore , it is proved in this Case , as required , that The ...
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Common terms and phrases
ABC and ABD AC and CD adjacent angles alternate angle angle ABC angle ACB angle AGH angle BAC angle CEB angle DEF angle EDF angle GHD Arithmetic BA and AC base BC Beginners bisected CONSTRUCTION.-1 crown 8vo Dictionary double the square draw Edition English Grammar English History equilateral Euclid exterior angle Gallic War Geography given straight line gnomon greater Greek half a right i.e. the angle interior and opposite join Latin Let ABC line be divided LONGMANS Manual note 2 def opposite angle parallel parallelogram post 8vo produced PROOF.-Because Proposition proved Q. E. D. Exercise Q. E. D. PROP rectangle contained rectilineal figure right angles School side AB side AC small 8vo square on AC Stepping-Stone straight line CD THEOREM triangle ABC twice the rect twice the rectangle vols Wherefore
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.