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 59
To describe a square upon a given straight line . Let AB be the given straight line . It is required to describe a square upon AB . D A B Construction . From the point A draw AC at right angles to AB ( I. 11 ) ; make AD equal to AB ( I.
To describe a square upon a given straight line . Let AB be the given straight line . It is required to describe a square upon AB . D A B Construction . From the point A draw AC at right angles to AB ( I. 11 ) ; make AD equal to AB ( I.
Seite 61
On BC describe the square BDEC ( I. 46 ) ; and on BA , AC , the squares GB , HC ; through A draw AL parallel to BD or CE ( I. 31 ) , and join AD , FC . Demonstration . Then because the angle BAC is a right angle ( hyp . ) ...
On BC describe the square BDEC ( I. 46 ) ; and on BA , AC , the squares GB , HC ; through A draw AL parallel to BD or CE ( I. 31 ) , and join AD , FC . Demonstration . Then because the angle BAC is a right angle ( hyp . ) ...
Seite 62
The whole square BDEC is equal to the two squares GB , HC ( Ax . 2 ) ; and the square BDEC is described upon the straight line BC , and the squares GB , HC upon AB , AC ; therefore 10. The square upon the side BC is equal to the squares ...
The whole square BDEC is equal to the two squares GB , HC ( Ax . 2 ) ; and the square BDEC is described upon the straight line BC , and the squares GB , HC upon AB , AC ; therefore 10. The square upon the side BC is equal to the squares ...
Seite 63
Let the square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other two sides , AB , AC . B Then the angle BAC shall be a right angle . Construction . From the point A draw AD at right angles ...
Let the square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other two sides , AB , AC . B Then the angle BAC shall be a right angle . Construction . From the point A draw AD at right angles ...
Seite 66
Then the rectangle contained by AB , BC , together with that contained by AB , AC , shall be equal to the square on AB . A D F E Construction . Upon AB describe the square ADEB ( I. 46 ) , and through C draw CF parallel to AD or BE ( I.
Then the rectangle contained by AB , BC , together with that contained by AB , AC , shall be equal to the square on AB . A D F E Construction . Upon AB describe the square ADEB ( I. 46 ) , and through C draw CF parallel to AD or BE ( I.
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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
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
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 |