The College Euclid: Comprising the First Six and the Parts of the Eleventh and Twelfth Books Read at the Universities ... By A. K. Isbister1865 |
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Seite 15
... bisect a given rectilineal angle , that is , to divide it into two equal angles . ( References Prop . I. 1 , 3 , 8. ) Let the angle BAC be the given rectilineal angle . It is required to bisect it . A B F E CONSTRUCTION Take any point D ...
... bisect a given rectilineal angle , that is , to divide it into two equal angles . ( References Prop . I. 1 , 3 , 8. ) Let the angle BAC be the given rectilineal angle . It is required to bisect it . A B F E CONSTRUCTION Take any point D ...
Seite 16
... bisect a given finite straight line , that is , to divide it into two equal parts . ( References - Prop . I. 1 , 4 , 9. ) Let AB be the given straight line . It is required to divide AB into two equal parts . B D CONSTRUCTION Upon the ...
... bisect a given finite straight line , that is , to divide it into two equal parts . ( References - Prop . I. 1 , 4 , 9. ) Let AB be the given straight line . It is required to divide AB into two equal parts . B D CONSTRUCTION Upon the ...
Seite 19
... bisect FG in H , ( 1. 10 ) and join CF , CH , CG . Then the straight line CH , drawn from the point C , is perpendicular to the given straight line AB . DEMONSTRATION Because FH is equal to HG , ( constr . ) and HC common to the two ...
... bisect FG in H , ( 1. 10 ) and join CF , CH , CG . Then the straight line CH , drawn from the point C , is perpendicular to the given straight line AB . DEMONSTRATION Because FH is equal to HG , ( constr . ) and HC common to the two ...
Seite 23
... Bisect AC in E , ( 1. 10 ) and join BE , produce BE to F , and make EF equal to BE ; ( 1. 3 ) and join FC . DEMONSTRATION Because AE is equal to EC , and BE to EF ; the two sides AE , EB , are equal to the two CE , EF , each to each ...
... Bisect AC in E , ( 1. 10 ) and join BE , produce BE to F , and make EF equal to BE ; ( 1. 3 ) and join FC . DEMONSTRATION Because AE is equal to EC , and BE to EF ; the two sides AE , EB , are equal to the two CE , EF , each to each ...
Seite 42
... bisects them , that is , divides them into two equal parts . N.B. A parallelogram is a four - sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles ...
... bisects them , that is , divides them into two equal parts . N.B. A parallelogram is a four - sided figure , of which the opposite sides are parallel ; and the diameter is the straight line joining two of its opposite angles ...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisect Book centre circle ABC circumference compounded constr DEMONSTRATION diameter double draw Edition English equal angles equal straight lines equal to BC equiangular equilateral and equiangular equimultiples Euclid exterior angle four magnitudes fourth French given circle given point given rectilineal angle given straight line gnomon Grammar greater ratio inscribed isosceles triangle join less Let ABC multiple opposite angles parallel parallelogram pentagon perpendicular plane polygon proportionals proposition Q. E. D. PROP rectangle contained rectilineal figure References-Prop remaining angle right angles segment similar solid angle square of AC straight line AC THEOREM third three straight lines touches the circle triangle ABC twice the rectangle wherefore
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Seite 140 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite xiv - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Seite 310 - 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.
Seite 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite vi - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Seite 310 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite xxxvii - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Seite 287 - If any point be taken in the diameter of a circle which is not the centre, of all the straight lines which can be drawn from it to the circumference, the greatest is that in which the centre is, and the other part of that diameter is the least...