## 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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Resultat 1-5 av 9

Side 154

Triangles and parallelograms of the same altitude are one to another as their

straight lines BG , GH , each equal to the

them ...

Triangles and parallelograms of the same altitude are one to another as their

**bases**. ... Produce BD both ways to the points H , L , and take any number ofstraight lines BG , GH , each equal to the

**base**BC ; and DK , KL , any number ofthem ...

Side 238

is the

and as the solid CD to CV , so ( 25. 11. ) ... Wherefore , the

parallelopipeds AB , CD are reciprocally proportional to their altitudes . Let now

the ...

is the

**base**EH to the**base**NP ; for the solids AB , CV are of the same altitude ;and as the solid CD to CV , so ( 25. 11. ) ... Wherefore , the

**bases**of the solidparallelopipeds AB , CD are reciprocally proportional to their altitudes . Let now

the ...

Side 239

Let the insisting straight lines FE , BL , GA , KH ; XN , DO , MC , RP not be at right

angles to the

their altitudes , viz . the

...

Let the insisting straight lines FE , BL , GA , KH ; XN , DO , MC , RP not be at right

angles to the

**bases**of the solids ... their**bases**are reciprocally proportional totheir altitudes , viz . the

**base**EH to the**base**NP , as the altitude of the solid CD to...

Side 259

same altitude ; and therefore as the

triangle ABC to the triangle DEF , so ( Cor . 32. 11. ) is the prism having the

triangle LXC for its

which the ...

same altitude ; and therefore as the

**base**LXC to the**base**RVF ; that is , as thetriangle ABC to the triangle DEF , so ( Cor . 32. 11. ) is the prism having the

triangle LXC for its

**base**, and OMN the triangle opposite to it , to the prism ofwhich the ...

Side 263

as the

FGHKLN . Therefore ... EVERY prism having a triangular

into three pyramids that have triangular

as the

**base**ABCDE to the**base**FGHKL , so the pyramid ABCDEM to the pyramidFGHKLN . Therefore ... EVERY prism having a triangular

**base**, may be dividedinto three pyramids that have triangular

**bases**, and are equal to one another .### 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.