Euclid for beginners, books i. and ii., with simple exercises by F.B. HarveyLongmans, Green, and Company, 1880 - 119 sider |
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Side 32
... third . Let A , B , and C be three given lines any two of which are together greater than the third . It is required to make a triangle having its sides A , B , and C , each to each . D F G HE L A B CONSTRUCTION .-- 1 . Take a straight ...
... third . Let A , B , and C be three given lines any two of which are together greater than the third . It is required to make a triangle having its sides A , B , and C , each to each . D F G HE L A B CONSTRUCTION .-- 1 . Take a straight ...
Side 34
... third sides shall be unequal , and the base of that triangle which has the greater angle shall be greater than the base of the other . Let ABC and DEF be two triangles , with the sides AB and AC in the former = the sides DE and DF , in ...
... third sides shall be unequal , and the base of that triangle which has the greater angle shall be greater than the base of the other . Let ABC and DEF be two triangles , with the sides AB and AC in the former = the sides DE and DF , in ...
Side 36
... third sides unequal to each other , then the angles contained by the equal sides in each triangle shall be unequal , and the angle contained by the two sides of that triangle which has the greater base shall be greater than the angle ...
... third sides unequal to each other , then the angles contained by the equal sides in each triangle shall be unequal , and the angle contained by the two sides of that triangle which has the greater base shall be greater than the angle ...
Side 38
... third angle in the former triangle = the third angle in the latter . CASE I. First , let the given equal sides be those adjacent to the equal angles in each triangle , viz . BC and EF . Then it is to be proved that 1. The other two ...
... third angle in the former triangle = the third angle in the latter . CASE I. First , let the given equal sides be those adjacent to the equal angles in each triangle , viz . BC and EF . Then it is to be proved that 1. The other two ...
Side 39
... third angle BAC in the former triangle third angle EDF in the latter . the Q. E. D. Exercises . Prove the above Case- 1. By supposing DE to be greater than AB . 2. By supposing AC to be greater than DF . 3. By supposing DF to be greater ...
... third angle BAC in the former triangle third angle EDF in the latter . the Q. E. D. Exercises . Prove the above Case- 1. By supposing DE to be greater than AB . 2. By supposing AC to be greater than DF . 3. By supposing DF to be greater ...
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Euclid for beginners, books i. and ii., with simple exercises by F.B. Harvey Euclides,Frederick Burn Harvey Uten tilgangsbegrensning - 1880 |
Euclid for Beginners, Books I. and II., with Simple Exercises by F.B. Harvey Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 14 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Side 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.
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.