Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey |
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Page 75
... double the triangle ABD ( I. 41 ) . And , for the same reason , the square GB is double the triangle FBC . But , as we have proved , the triangle ABD the triangle FBC ; therefore the parallelogram BL = the square GB ( ax . 6 ) . = In ...
... double the triangle ABD ( I. 41 ) . And , for the same reason , the square GB is double the triangle FBC . But , as we have proved , the triangle ABD the triangle FBC ; therefore the parallelogram BL = the square GB ( ax . 6 ) . = In ...
Page 98
... two equal and also into two unequal parts , the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section . Let AB be a straight line divided into two ...
... two equal and also into two unequal parts , the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section . Let AB be a straight line divided into two ...
Page 100
... double the square on AC , therefore the squares on EA and EF = double the squares on AC and CD ( ax . 2 ) . G C B 6. Next , because in the triangle AEF the square on AF = the squares on EA and EF ( I. 47 ) , therefore the square on AF ...
... double the square on AC , therefore the squares on EA and EF = double the squares on AC and CD ( ax . 2 ) . G C B 6. Next , because in the triangle AEF the square on AF = the squares on EA and EF ( I. 47 ) , therefore the square on AF ...
Page 101
... square on EF double the square on CD ( as in 5 ) ; and to prove that the squares on AE and EF double the squares on AC and CD . = f . In triangle AEF to prove that the square on AF = double the squares on AC and CD ( as in 6 ) . g . In ...
... square on EF double the square on CD ( as in 5 ) ; and to prove that the squares on AE and EF double the squares on AC and CD . = f . In triangle AEF to prove that the square on AF = double the squares on AC and CD ( as in 6 ) . g . In ...
Page 102
... square on the part of it produced , are together double of the square on half the line bisected and of the square on the line made up of the half and the part produced . Let AB be a straight line bisected in C , and produced to D. Then ...
... square on the part of it produced , are together double of the square on half the line bisected and of the square on the line made up of the half and the part produced . Let AB be a straight line bisected in C , and produced to D. Then ...
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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.