The Elements of Geometry, Symbolically Arranged |
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Seite 41
E B D A F с AD meets BC , EF , and makes alt . EAD = alt . △ ADC , .. EF || BC . Therefore , a str . line has been drawn through A || BC . Prop . 26 . Prop . 22 . Prop . 26 . PROP . XXXI . THEOR . 32. 1 Eu . D 3 PROP . XXIX . XXX .
E B D A F с AD meets BC , EF , and makes alt . EAD = alt . △ ADC , .. EF || BC . Therefore , a str . line has been drawn through A || BC . Prop . 26 . Prop . 22 . Prop . 26 . PROP . XXXI . THEOR . 32. 1 Eu . D 3 PROP . XXIX . XXX .
Seite 42
Again , Draw CE AB ; AC meets them , alt . BAC = alt . ACE . :: BD falls upon the || lines AB , CE , Prop . 28 . ext . L ECD = { Z ABC , the int . and oppo . ; but LACE BAC . L BAC + 2 .. whole ext . / ACD = Ax . 2 ABC , to each of ...
Again , Draw CE AB ; AC meets them , alt . BAC = alt . ACE . :: BD falls upon the || lines AB , CE , Prop . 28 . ext . L ECD = { Z ABC , the int . and oppo . ; but LACE BAC . L BAC + 2 .. whole ext . / ACD = Ax . 2 ABC , to each of ...
Seite 44
Let AB , CD , be and | str . lines , joined towards the same parts by the str . lines AC , BD : then shall AC and BD be = and [ ] to each other . A B с Join BC . D AB || CD and BC meets them , ..alt . ABC alt .
Let AB , CD , be and | str . lines , joined towards the same parts by the str . lines AC , BD : then shall AC and BD be = and [ ] to each other . A B с Join BC . D AB || CD and BC meets them , ..alt . ABC alt .
Seite 45
JBC meets AC , BD , and makes alt . ACB alt . CBD , AC || BD : Prop . 26 . and it has been proved that ACBD . Therefore str . lines , & c . PROP . XXXIII . THEOR . 34. 1 Eu . The opposite sides and angles of parallelo- grams are equal ...
JBC meets AC , BD , and makes alt . ACB alt . CBD , AC || BD : Prop . 26 . and it has been proved that ACBD . Therefore str . lines , & c . PROP . XXXIII . THEOR . 34. 1 Eu . The opposite sides and angles of parallelo- grams are equal ...
Seite 52
Also AD meets the || s AB , DE , TM , Prop . 28 . :: < BAD + △ ADE = 2 rt . s Constr . Ax . 3 . Prop . 33 . Ax . 1 . but BAD is a rt . ; ZADE is a rt . ; but opp.s of are equal , .. ms thes ABE , BED , are rt .
Also AD meets the || s AB , DE , TM , Prop . 28 . :: < BAD + △ ADE = 2 rt . s Constr . Ax . 3 . Prop . 33 . Ax . 1 . but BAD is a rt . ; ZADE is a rt . ; but opp.s of are equal , .. ms thes ABE , BED , are rt .
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The Elements of Geometry, Symbolically Arranged Great Britain Admiralty Keine Leseprobe verfügbar - 2016 |
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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
Beliebte Passagen
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.
Bibliografische Informationen
| Titel | The Elements of Geometry, Symbolically Arranged |
| Autor/in | Great Britain. Admiralty |
| Ausgabe | 2 |
| Veröffentlicht | 1846 |
| Original von | Oxford University |
| Digitalisiert | 10. Okt. 2006 |
| Zitat exportieren | BiBTeX EndNote RefMan |