The Elements of Geometry, Symbolically Arranged |
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Seite 14
... BC coincides with EF . For if BC do not coincide with EF , then two Ax . 10. str . lines enclose a space , which is ... base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the ...
... BC coincides with EF . For if BC do not coincide with EF , then two Ax . 10. str . lines enclose a space , which is ... base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the ...
Seite 18
... BC common to both as ; base AB , DBC = △ ACB , base DC Prop . 4 . and or , the less .. { the greater , which is AB is not AC , i . e . AB AC . Wherefore , if two angles , & c . COR . - Hence every equiangular triangle is equilateral ...
... BC common to both as ; base AB , DBC = △ ACB , base DC Prop . 4 . and or , the less .. { the greater , which is AB is not AC , i . e . AB AC . Wherefore , if two angles , & c . COR . - Hence every equiangular triangle is equilateral ...
Seite 26
... base AB = base CF , L BAC / ECF , Prop . 14 . Prop . 4 . Ax . 9 . but .. < ACD > BAC . Prop . 14 . ACD > < ECF ; In the same way , if BC be bisected , and AC be prod . to G , it may be shown , that Z BCG or ACD > Therefore , if one side ...
... base AB = base CF , L BAC / ECF , Prop . 14 . Prop . 4 . Ax . 9 . but .. < ACD > BAC . Prop . 14 . ACD > < ECF ; In the same way , if BC be bisected , and AC be prod . to G , it may be shown , that Z BCG or ACD > Therefore , if one side ...
Seite 32
... shall be greater than the base of the other . = Let ABC , DEF , be two As , having the sides AB , AC : sides DE , DF , ea . to ea . , but △ BAC > < EDF : then , base BC > base EF . D B C E F Of the sides DE , 32 GEOMETRY .
... shall be greater than the base of the other . = Let ABC , DEF , be two As , having the sides AB , AC : sides DE , DF , ea . to ea . , but △ BAC > < EDF : then , base BC > base EF . D B C E F Of the sides DE , 32 GEOMETRY .
Seite 33
... BC , :: BC > EF . Therefore , if two triangles , & c . PROP . XXIV . THEOR . 25. 1 Eu . If two triangles have two sides of the one , equal to two sides of the other , each to each , but the base of the one , greater than the base of the ...
... BC , :: BC > EF . Therefore , if two triangles , & c . PROP . XXIV . THEOR . 25. 1 Eu . If two triangles have two sides of the one , equal to two sides of the other , each to each , but the base of the one , greater than the base of the ...
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The Elements of Geometry, Symbolically Arranged Great Britain Admiralty Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD AC² angle contained base base BC bisect called centre circle circumference coincides common Constr descr described diam diameter dist divided draw equal equal angles equiangular equilat expressed extremities falls figure given point given straight line gnomon greater half isosceles join less Let ABC line drawn manner mean meet oppo opposite angle opposite sides parallel parallelogram pass perpendicular plane polygon PROB prod produced Prop proportional proposition proved quantities ratio rect rectangle contained rectilineal remain right angles segments shown sides square THEOR touch triangle unequal Wherefore Нур
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Seite 58 - 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.
Seite 32 - 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 60 - 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...
Seite 36 - 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...
Seite 61 - 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.
Seite 21 - 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.
Seite 37 - 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...
Seite 3 - 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.
Seite 77 - 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.
Seite 19 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.