The Elements of Geometry, Symbolically Arranged |
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Seite 26
Prop . 15 . ext . oppo . ; B C D Produce BC to D. ACD > ABC , the int . and add 2 ACD + ACD + 2 Prop . 12. but :: Z ABC + ≤ ACB to each , ACB > ABC + ACB ; ACB = 2 rt . ≤s , ACB < 2 rt . s . In like manner it may be proved , that BAC ...
Prop . 15 . ext . oppo . ; B C D Produce BC to D. ACD > ABC , the int . and add 2 ACD + ACD + 2 Prop . 12. but :: Z ABC + ≤ ACB to each , ACB > ABC + ACB ; ACB = 2 rt . ≤s , ACB < 2 rt . s . In like manner it may be proved , that BAC ...
Seite 27
In like manner it may be proved , that BAC + ACB < 2 rt . LS , and CAB + ≤ ABC < 2 rt . Therefore , any two angles , & c . s . PROP . XVII . THEOR . 18. 1 Eu . The greater side of every triangle is opposite to , or subtends the greater ...
In like manner it may be proved , that BAC + ACB < 2 rt . LS , and CAB + ≤ ABC < 2 rt . Therefore , any two angles , & c . s . PROP . XVII . THEOR . 18. 1 Eu . The greater side of every triangle is opposite to , or subtends the greater ...
Seite 30
But it has been proved BA + AC > BE + EC , much more then is BA + AC > CD + DB . Prop . 15. Again , in △ CDE , ext . △ BDC > int . / CED , and in ABE , ext . / CED > int , △ BAC , much more then is < BDC > Therefore , if from the ...
But it has been proved BA + AC > BE + EC , much more then is BA + AC > CD + DB . Prop . 15. Again , in △ CDE , ext . △ BDC > int . / CED , and in ABE , ext . / CED > int , △ BAC , much more then is < BDC > Therefore , if from the ...
Seite 33
DFG DGF ; Ax . 9 . but DGF > EGF , DFG > EGF , .. much more is EFG > < EGF , :: EG > EF ; but it was proved that EG = BC , :: BC > EF . Therefore , if two triangles , & c . PROP . XXIV . THEOR . 25. 1 Eu . If two triangles have two ...
DFG DGF ; Ax . 9 . but DGF > EGF , DFG > EGF , .. much more is EFG > < EGF , :: EG > EF ; but it was proved that EG = BC , :: BC > EF . Therefore , if two triangles , & c . PROP . XXIV . THEOR . 25. 1 Eu . If two triangles have two ...
Seite 34
If BAC < △ EDF , .. base BC < base EF , which is not true ; BAC EDF ; and it has been proved △ BAC / EDF , :: BAC > < EDF . Wherefore , if two triangles , & c . PROP . XXV . THEOR . 26. 1Eu . If two triangles have two angles of the ...
If BAC < △ EDF , .. base BC < base EF , which is not true ; BAC EDF ; and it has been proved △ BAC / EDF , :: BAC > < EDF . Wherefore , if two triangles , & c . PROP . XXV . THEOR . 26. 1Eu . If two triangles have two angles of the ...
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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
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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.
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 |