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 38
If a straight line falling on two other straight lines , make the alternate angles equal to each other ; these two straight lines shall be parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the ...
If a straight line falling on two other straight lines , make the alternate angles equal to each other ; these two straight lines shall be parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the ...
Seite 39
The angle AGH is equal to the angle GHD ( Ax . 1 ) , and they are alternate angles ; therefore 2. AB is parallel to CD ( I. 27 ) . Again , because the angles BGH , GHD are together equal to two right angles ( hyp . ) ...
The angle AGH is equal to the angle GHD ( Ax . 1 ) , and they are alternate angles ; therefore 2. AB is parallel to CD ( I. 27 ) . Again , because the angles BGH , GHD are together equal to two right angles ( hyp . ) ...
Seite 40
Then the alternate angles AGH , GHD shall be equal to one another ; the exterior angle EGB shall be equal to the interior and opposite angle GHD upon the same side of the line EF ; and the two interior angles BGH , ĜHD upon the same ...
Then the alternate angles AGH , GHD shall be equal to one another ; the exterior angle EGB shall be equal to the interior and opposite angle GHD upon the same side of the line EF ; and the two interior angles BGH , ĜHD upon the same ...
Seite 41
А B E Construction . Let the straight line GHK cut AB , EF , CD . Demonstration . Then because GHK cuts the parallel straight lines AB , EF , in G , H , therefore 1. The angle AGH is equal to the alternate angle GHF ( I. 29 ) .
А B E Construction . Let the straight line GHK cut AB , EF , CD . Demonstration . Then because GHK cuts the parallel straight lines AB , EF , in G , H , therefore 1. The angle AGH is equal to the alternate angle GHF ( I. 29 ) .
Seite 42
Because the straight line AD meets the two straight lines EF , BC , and makes the alternate angles EAD , ADC equal to one another , therefore EF is parallel to BC ( I. 27 ) . Wherefore , through the given point A , a straight line EAF ...
Because the straight line AD meets the two straight lines EF , BC , and makes the alternate angles EAD , ADC equal to one another , therefore EF is parallel to BC ( I. 27 ) . Wherefore , through the given point A , a straight line EAF ...
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The Elements of Euclid, Containing the First Six Books, with a Selection of ... Euclides Keine Leseprobe verfügbar - 2016 |
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ABCD AC is equal alternate angle ABC angle ACB angle BAC base base BC bisected centre circle ABC circumference common compounded constr Construction contained Demonstration describe diameter divided double draw equal angles equiangular equimultiples exterior angle extremities fall figure four fourth given point given straight line greater half inscribed interior join less Let ABC likewise magnitudes manner meet multiple opposite angle parallel parallelogram pass perpendicular plane polygon Problem produced proportionals proved Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar square square on AC taken third touches the circle triangle ABC unequal wherefore whole
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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 |