Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey |
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Page vi
Euclides, Frederick Burn Harvey. be proved in the Proposition , will be found to contribute ma- terially to the advantages spoken of . provement is sought in the further inclusive , of red ink , to denote the ' construction ' of the ...
Euclides, Frederick Burn Harvey. be proved in the Proposition , will be found to contribute ma- terially to the advantages spoken of . provement is sought in the further inclusive , of red ink , to denote the ' construction ' of the ...
Page ix
... proved , as that the angles at the base of an Isosceles Triangle are equal to each other . But in Problems as well ... prove the accu- racy of our work . Every Proposition , therefore , is to be considered as a process of reasoning ...
... proved , as that the angles at the base of an Isosceles Triangle are equal to each other . But in Problems as well ... prove the accu- racy of our work . Every Proposition , therefore , is to be considered as a process of reasoning ...
Page x
... proved , which is printed here in red type . 2. The Construction is the addition to the lines or figures , originally given , of such other lines , or figures , as are neces- sary to the argument required . These Construction lines and ...
... proved , which is printed here in red type . 2. The Construction is the addition to the lines or figures , originally given , of such other lines , or figures , as are neces- sary to the argument required . These Construction lines and ...
Page xvi
... proved that arc BC is the same part of its cir- cumference that DE is of its circumference . Therefore the angle BAC = the angle DAE , and hence— 2. The length of the arms of an angle makes no difference in the magnitude of that angle ...
... proved that arc BC is the same part of its cir- cumference that DE is of its circumference . Therefore the angle BAC = the angle DAE , and hence— 2. The length of the arms of an angle makes no difference in the magnitude of that angle ...
Page 2
... proved that AL is the line drawn from A = BC . PROOF . - Because B is the centre of the circle CHG , therefore BG BC ( def . 15 ) . Similarly , because D is the centre of the circle GKL , therefore DG = DL . But in the lines DG and DL ...
... proved that AL is the line drawn from A = BC . PROOF . - Because B is the centre of the circle CHG , therefore BG BC ( def . 15 ) . Similarly , because D is the centre of the circle GKL , therefore DG = DL . But in the lines DG and DL ...
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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.