The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
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Seite 11
Let AB and C be the two given straight lines , of which AB is the greater . It is required to cut off from AB the greater , a part equal to C the less . D 3 A F Construction . From the point A draw the straight line AD equal to C ( I. 2 ) ...
Let AB and C be the two given straight lines , of which AB is the greater . It is required to cut off from AB the greater , a part equal to C the less . D 3 A F Construction . From the point A draw the straight line AD equal to C ( I. 2 ) ...
Seite 14
For , if AB be not equal to AC , one of them is greater than the other . If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the less ( I. 3 ) , and join DC . * An abbreviation for quod erat demonstrandum - that ...
For , if AB be not equal to AC , one of them is greater than the other . If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the less ( I. 3 ) , and join DC . * An abbreviation for quod erat demonstrandum - that ...
Seite 16
But the angle ACD is greater than the angle BCD ( Ax . 9 ) ; therefore also 2. The angle ADC is greater than BCD ; much more therefore 3. The angle BDC is greater than the angle BCD . Again , because the side BC is equal to BD in the ...
But the angle ACD is greater than the angle BCD ( Ax . 9 ) ; therefore also 2. The angle ADC is greater than BCD ; much more therefore 3. The angle BDC is greater than the angle BCD . Again , because the side BC is equal to BD in the ...
Seite 17
The angles ECD , FDC are equal to one another ( I. 5 ) ; but the angle ECD greater than the angle BCD ( Ax . 9 ) ; therefore also 2. The angle FDC is greater than the angle BCD ; much more then 3. The angle BDC is greater than the angle ...
The angles ECD , FDC are equal to one another ( I. 5 ) ; but the angle ECD greater than the angle BCD ( Ax . 9 ) ; therefore also 2. The angle FDC is greater than the angle BCD ; much more then 3. The angle BDC is greater than the angle ...
Seite 21
The angle EBD is equal to the angle EBC ( Ax . 1 ) , the less equal to the greater angle , which is impossible . Therefore , 4. Two straight lines cannot have a common segment . PROPOSITION 12.- Problem .
The angle EBD is equal to the angle EBC ( Ax . 1 ) , the less equal to the greater angle , which is impossible . Therefore , 4. Two straight lines cannot have a common segment . PROPOSITION 12.- Problem .
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
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Beliebte Passagen
Seite 4 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 230 - If two triangles, which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another, the remaining sides shall be in a straight line. Let...
Seite 110 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 207 - ... triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Seite 267 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Seite 197 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 21 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Seite 61 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Seite 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Bibliografische Informationen
| Titel | The Elements of Euclid, containing the first six books, with a selection of geometrical problems. To which is added the parts of the eleventh and twelfth books which are usually read at the universities. By J. Martin |
| Autor/in | Euclides |
| Herausgeber | James Martin (of the Wedgwood inst, Burslem) |
| Veröffentlicht | 1874 |
| Original von | Oxford University |
| Digitalisiert | 8. Sept. 2006 |
| Zitat exportieren | BiBTeX EndNote RefMan |