The Elements of Geometry, Symbolically Arranged |
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Σελίδα 13
... sides are opposite . = Let ABC , DEF , be two As , of which AB = DE , AC DF , and BAC = EDF . Then BC EF , △ ABC = △ DEF , L ABCDEF , and Z ACB = ≤ DFE . Def . 15 . Constr . Ax . 1 . D Нур . B For if that pt . A PROP . IV . 13.
... sides are opposite . = Let ABC , DEF , be two As , of which AB = DE , AC DF , and BAC = EDF . Then BC EF , △ ABC = △ DEF , L ABCDEF , and Z ACB = ≤ DFE . Def . 15 . Constr . Ax . 1 . D Нур . B For if that pt . A PROP . IV . 13.
Σελίδα 14
Great Britain. Admiralty. D Нур . B For if that pt . A may Hyp . Нур . And But CE F ABC be applied to △ DEF , so be on D , and AB on DE . AB = DE , B coincides with E. AB concides with DE , BACEDF ; AC falls upon DF . AC = DF , C ...
Great Britain. Admiralty. D Нур . B For if that pt . A may Hyp . Нур . And But CE F ABC be applied to △ DEF , so be on D , and AB on DE . AB = DE , B coincides with E. AB concides with DE , BACEDF ; AC falls upon DF . AC = DF , C ...
Σελίδα 34
... Нур . If / BAC < / EDF , .. base BC < base EF , which is not true ; BAC EDF ; and it has been proved / BAC # △ EDF , .. < BAC > Wherefore , if two triangles , & c . EDF . PROP . XXV . THEOR . 26. 1Eu . If two triangles have two angles ...
... Нур . If / BAC < / EDF , .. base BC < base EF , which is not true ; BAC EDF ; and it has been proved / BAC # △ EDF , .. < BAC > Wherefore , if two triangles , & c . EDF . PROP . XXV . THEOR . 26. 1Eu . If two triangles have two angles ...
Σελίδα 36
... Нур . Ax . 1 . BHA / EFD ; but △ BCA EFD , .. △ BHA = △ BCA , i . e . ext . AHC , of BHA - BCA , the int . and oppo . 2 , Prop . 15 . i . e . Then : Hyp . △ ABC base AC which is impossible , BC is not EF , BC = EF . AB , BC = DE ...
... Нур . Ax . 1 . BHA / EFD ; but △ BCA EFD , .. △ BHA = △ BCA , i . e . ext . AHC , of BHA - BCA , the int . and oppo . 2 , Prop . 15 . i . e . Then : Hyp . △ ABC base AC which is impossible , BC is not EF , BC = EF . AB , BC = DE ...
Σελίδα 44
... AC and BD be = and to each other . A B Prop . 28 . Нур . C Join BC . D AB || CD and BC meets them , .. alt . ABC { - alt . BCD ; AB = CD , BC common to s ABC , DCB , △ BCD , Z ABC = base AC base BD , .. { △ ACB = 44 GEOMETRY .
... AC and BD be = and to each other . A B Prop . 28 . Нур . C Join BC . D AB || CD and BC meets them , .. alt . ABC { - alt . BCD ; AB = CD , BC common to s ABC , DCB , △ BCD , Z ABC = base AC base BD , .. { △ ACB = 44 GEOMETRY .
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The Elements of Geometry, Symbolically Arranged Great Britain Admiralty Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
2ndly ABCD AC² angle contained angle equal base BC CB² centre circle circumference coincides Constr descr diam diameter dist divided equal angles equiangular equilat exterior angle figure given point given str given straight line gnomon greater isosceles triangle join Let ABC Let str Let the str line be drawn meet number of equal oppo opposite angle opposite sides parallel parallelogram perpendicular polygon PROB prod Prop rect rectangle contained rectilineal right angles right-angled triangle semi sides equal square THEOR touch trapezium Wherefore whole fig Нур
Δημοφιλή αποσπάσματα
Σελίδα 60 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 34 - 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...
Σελίδα 62 - If a straight 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...
Σελίδα 38 - Wherefore, if a straight line, &c. QB D. PROPOSITION XXVIII. THEOB.—-If a straight line, falling upon two other straight lines, make the exterior angle equal to...
Σελίδα 63 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 23 - 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.
Σελίδα 39 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Σελίδα 5 - 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 : XVI.
Σελίδα 79 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 21 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.