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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Side 64
EVERY right - angled parallelogram is called a rectangle , and is said to be
contained by any two of the straight lines which contain one of the right angles . 2
. In every parallelogram , any of the parallelograms about a diameter , together
with ...
EVERY right - angled parallelogram is called a rectangle , and is said to be
contained by any two of the straight lines which contain one of the right angles . 2
. In every parallelogram , any of the parallelograms about a diameter , together
with ...
Side 65
Let A and BC be two straight lines ; and let BC be divided into any parts BD , DE ,
EC , in the points D , E. Then the rectangle contained by the straight lines A and
BC shall be equal to the rectangle contained by A and BD , together with that ...
Let A and BC be two straight lines ; and let BC be divided into any parts BD , DE ,
EC , in the points D , E. Then the rectangle contained by the straight lines A and
BC shall be equal to the rectangle contained by A and BD , together with that ...
Side 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. 31 ) ...
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. 31 ) ...
Side 67
The rectangle AE is equal to the rectangles AD , CE . And 2. AE is the rectangle
contained by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ;
and 3. AD is contained by AC , CB , for CD is equal to CB ( Def . 30 ) , and CE is ...
The rectangle AE is equal to the rectangles AD , CE . And 2. AE is the rectangle
contained by AB , BC , for it is contained by AB , BE , of which BE is equal to BC ;
and 3. AD is contained by AC , CB , for CD is equal to CB ( Def . 30 ) , and CE is ...
Side 68
It is likewise rectangular ; for , since CG is parallel to BK , and BC meets them ,
therefore 6. The angles KBC , BCG are equal to two ... AG is the rectangle
contained by AC , CB ; for GC is equal to CB ; therefore also 13. 68 EUCLID'S
ELEMENTS .
It is likewise rectangular ; for , since CG is parallel to BK , and BC meets them ,
therefore 6. The angles KBC , BCG are equal to two ... AG is the rectangle
contained by AC , CB ; for GC is equal to CB ; therefore also 13. 68 EUCLID'S
ELEMENTS .
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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...
Side 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...
Side 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.
Side 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.
Side 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'.
Side 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.
Side 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.
Side 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...
Side 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.
Bibliografisk informasjon
| Tittel | 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 |
| Forfatter | Euclides |
| Redaktør | James Martin (of the Wedgwood inst, Burslem) |
| distribuert | 1874 |
| Original fra | Oxford University |
| Digitalisert | 8. sep 2006 |
| Eksporter sitat | BiBTeX EndNote RefMan |