## 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 |

### Inni boken

Resultat 1-5 av 9

Side 227

If a solid parallelopiped be cut by a plane passing through the diagonals of two of

the

parallelopiped , and DE , CF the diagonals of the

GB ...

If a solid parallelopiped be cut by a plane passing through the diagonals of two of

the

**opposite**planes ; it shall be cut in two equal parts . * Let AB be a solidparallelopiped , and DE , CF the diagonals of the

**opposite**parallelograms AH ,GB ...

Side 228

First , let the parallelograms DG , HN , which are

common side HG : then , because the solid AH is cut by the plane AGHC passing

through the diagonals AG , CH of the

First , let the parallelograms DG , HN , which are

**opposite**to the base AB , have acommon side HG : then , because the solid AH is cut by the plane AGHC passing

through the diagonals AG , CH of the

**opposite**planes ALGF , CBHD , AH is cut ... Side 257

base , and the straight line KH

triangle GFC for its base , and the triangle HKL

same altitude , because they are between the parallel ( 15. 11. ) planes ABC ,

HKL ...

base , and the straight line KH

**opposite**to it , is equal to the prism having thetriangle GFC for its base , and the triangle HKL

**opposite**to it ' ; for they are of thesame altitude , because they are between the parallel ( 15. 11. ) planes ABC ,

HKL ...

Side 259

is the prism having the triangle LXC for its base , and OMN the triangle

to it , to the prism of which the base is the triangle RVF , and the

STY : and because the two prisms in the pyramid ABCG are equal to one ...

is the prism having the triangle LXC for its base , and OMN the triangle

**opposite**to 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 297

B. I. This definition has one condition more than is necessary ; because every

quadrilateral figure which has its

likewise its

quadrilateral ...

B. I. This definition has one condition more than is necessary ; because every

quadrilateral figure which has its

**opposite**sides equal to one another , haslikewise its

**opposite**angles equal , and on the contrary . Let ABCD be aquadrilateral ...

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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.