## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |

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Side 249

If there be two triangular

a parallelogram , and the base of the ... for its base ; if the parallelogram AF be

double of the triangle GHK , the

If there be two triangular

**prisms**of the same altitude , the base of one of which isa parallelogram , and the base of the ... for its base ; if the parallelogram AF be

double of the triangle GHK , the

**prism**ABCDEF is equal to the**prism**GHKLMN . Side 257

base , and the straight line KH opposite to it , is equal to the

triangle GFC for its base , and the triangle HKL ... planes ABC , HKL : and it is

manifest that each of these

the ...

base , and the straight line KH opposite to it , is equal to the

**prism**having thetriangle GFC for its base , and the triangle HKL ... planes ABC , HKL : and it is

manifest that each of these

**prisms**is greater than either of the pyramids of whichthe ...

Side 259

is the

to it , to the

STY : and because the two

is the

**prism**having the triangle LXC for its base , and OMN the triangle oppositeto it , to the

**prism**of which the base is the triangle RVF , and the opposite triangleSTY : and because the two

**prisms**in the pyramid ABCG are equal to one ... Side 264

be a third part of the

DEF is the opposite triangle ; therefore the pyramid of which the base is the

triangle ABC , and vertex the point D , is the third part of the

same ...

be a third part of the

**prism**, the base of which is the triangle ABC , and to whichDEF is the opposite triangle ; therefore the pyramid of which the base is the

triangle ABC , and vertex the point D , is the third part of the

**prism**which has thesame ...

Side 268

Upon the square ABCD erect a

the circle , and a

Upon the square ABCD erect a

**prism**of the same altitude with the cylinder ; this**prism**is greater than half of the cylinder : because if a square be described aboutthe circle , and a

**prism**erected upon the square , of the same altitude with the ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.