The school Euclid: comprising the first four books, by A.K. Isbister1863 |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 15
... bisect a given rectilineal angle , that is , to divide it into two equal angles . ( References Prop . 1. 1 , 3 , 8. ) Let the angle BAC be the given rectilineal angle . It is required to bisect it . A D E B F CONSTRUCTION Take any point ...
... bisect a given rectilineal angle , that is , to divide it into two equal angles . ( References Prop . 1. 1 , 3 , 8. ) Let the angle BAC be the given rectilineal angle . It is required to bisect it . A D E B F CONSTRUCTION Take any point ...
Σελίδα 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 . A 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 . A B D CONSTRUCTION Upon the ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 43
... bisect it . A B DEMONSTRATION Because AB is parallel to CD , and BC meets them , therefore the alternate angles ABC , BCD , are equal to one another ; ( 1. 29 ) and because AC is parallel to BD , and BC meets them , therefore the ...
... bisect it . A B DEMONSTRATION Because AB is parallel to CD , and BC meets them , therefore the alternate angles ABC , BCD , are equal to one another ; ( 1. 29 ) and because AC is parallel to BD , and BC meets them , therefore the ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles alternate angles angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre circle ABC constr CONSTRUCTION cuts the circle DEMONSTRATION describe a circle describe the circle diameter double equal angles equal straight lines equal to BC equiangular pentagon equilateral and equiangular equilateral triangle Euclid exterior angle Geography given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite isosceles triangle less Let ABC Let the straight Ludgate Hill opposite angles parallel parallelogram pentagon perpendicular post 8vo produced Q. E. D. PROP rectangle contained rectilineal figure References Prop References-Prop remaining angle right angles segment semicircle side BC square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle
Δημοφιλή αποσπάσματα
Σελίδα 94 - A CONSTRUCTION For, if not let it fall otherwise, if possible, as FGDB; let F be the centre of the circle ABC, and G the centre of ADE. Join AF and AG. DEMONSTRATION Because two sides of a triangle are together greater than the third side therefore AG, GF, are greater than FA;
Σελίδα 17 - and they are adjacent angles. But, ' when a straight line standing' on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle;' (def. 10) therefore each of the angles DCF, ECF, is a right angle. Wherefore, from the point C, in the straight line AB,
Σελίδα xvii - to the same two, and when the adjacent angles are equal, they are right angles. Prop. 32. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; the angles made by this line with the line touching the circle, shall be
Σελίδα ii - at right angles to a given straight line, from a given point in the same. Prop. 13. The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Prop. 14. If, at a point in a straight line, two other straight lines,
Σελίδα 2 - XV. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another. XVL And this point is called the centre of the circle.
Σελίδα ix - line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Σελίδα 118 - (i. 32) and when the adjacent angles are equal, they are right angles, (i. def. 10.) PROP. XXXII. —THEOREM. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; then the angles made by this line with the line
Σελίδα iii - to four right angles. Prop. 16. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Prop. 17. Any two angles of a triangle are together less than two right angles. Prop.
Σελίδα 47 - Wherefore, triangles, &c. QED PROP. XXXVIII THEOREM. Triangles upon equal bases and between the same parallels are equal to one another. (References — Prop. i. 31, 34, 36 ; ax. 7.) Let the triangles ABC, DEF, be on the equal bases BC, EF, and between the same parallels AD, BF. Then
Σελίδα 23 - two angles of a triangle are together less than two right angles. Then any two of its angles shall be together less than two right angles, A CONSTRUCTION Produce the side BC to D. DEMONSTRATION Because ACD is the exterior angle of the triangle ABC, therefore the angle ACD is greater than the interior and opposite angle