Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey |
From inside the book
Results 1-5 of 5
Page xxii
... coincide with one another — that is , which fill exactly the same space - are equal to one another . 9 . The whole is greater than its part . 10 . Two straight lines cannot enclose space . 11 . All right angles are equal to one another ...
... coincide with one another — that is , which fill exactly the same space - are equal to one another . 9 . The whole is greater than its part . 10 . Two straight lines cannot enclose space . 11 . All right angles are equal to one another ...
Page 4
... coincide with the side DE . Next , because the side AB coincides with the side DE , and because the angle BAC = the angle EDF ( hyp . ) , therefore the side AC shall fall on the side DF , and , because the point A coincides with the ...
... coincide with the side DE . Next , because the side AB coincides with the side DE , and because the angle BAC = the angle EDF ( hyp . ) , therefore the side AC shall fall on the side DF , and , because the point A coincides with the ...
Page 5
... coincides with the point E , and the point C coincides with the point F , then , if the whole base BC does not coincide with the whole base EF , we have two straight lines enclosing a space , which is impossible ( ax . 10 ) . Therefore ...
... coincides with the point E , and the point C coincides with the point F , then , if the whole base BC does not coincide with the whole base EF , we have two straight lines enclosing a space , which is impossible ( ax . 10 ) . Therefore ...
Page 12
... coincides with the side EF . Next , because the side BC coincides with the side EF therefore the sides BA and AC shall coincide with the sides ED and DF respectively . For , if BC coincides with EF , and then BA and AC do not coincide ...
... coincides with the side EF . Next , because the side BC coincides with the side EF therefore the sides BA and AC shall coincide with the sides ED and DF respectively . For , if BC coincides with EF , and then BA and AC do not coincide ...
Page 13
Euclides, Frederick Burn Harvey. Therefore , if BC coincides with EF , then BA and AC must coincide with ED and DF , and the angle BAC will coincide with , and equal , the angle EDF ( ax . 8 ) . Therefore , it is proved , as required ...
Euclides, Frederick Burn Harvey. Therefore , if BC coincides with EF , then BA and AC must coincide with ED and DF , and the angle BAC will coincide with , and equal , the angle EDF ( ax . 8 ) . Therefore , it is proved , as required ...
Other editions - View all
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.