## 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 5

Side 16

to the base GB , and the triangle AFC to the triangle AGB ; and the

angles of the one are equal ( 4. 1. ) to the

each , to which the equal f sides are opposite ; viz . the angle ACF to the angle

ABG ...

to the base GB , and the triangle AFC to the triangle AGB ; and the

**remaining**angles of the one are equal ( 4. 1. ) to the

**remaining**angles of the other , each toeach , to which the equal f sides are opposite ; viz . the angle ACF to the angle

ABG ...

Side 150

... then the ratio compounded of the

ratio of the first , if but one remain , is the same with the ratio compounded of

those

ratios ...

... then the ratio compounded of the

**remaining**ratios of the first , or the**remaining**ratio of the first , if but one remain , is the same with the ratio compounded of

those

**remaining**of the last , or with the**remaining**ratio of the last . * Let the firstratios ...

Side 161

At the points D , F , in the straight line DF , make ( 23. 1. ) the angle FDG equal to

either of the angles BAC , EDF ; and the angle DFG equal to the angle A ACB ;

wherefore the

. ) ...

At the points D , F , in the straight line DF , make ( 23. 1. ) the angle FDG equal to

either of the angles BAC , EDF ; and the angle DFG equal to the angle A ACB ;

wherefore the

**remaining**D angle at B is equal to the reG maining one at G ( 32. 1. ) ...

Side 162

IF two triangles have one angle of the one equal to one angle of the other , and

the sides about two other angles proportionals , then , if each of the

angles be either less , or not less , than a right angle ; or if one of them be a right

...

IF two triangles have one angle of the one equal to one angle of the other , and

the sides about two other angles proportionals , then , if each of the

**remaining**angles be either less , or not less , than a right angle ; or if one of them be a right

...

Side 242

to the base EF , and the

ABC is therefore equal to the angle DEF : and the right angle ABK is equal to the

right angle DEN , whence the

to the base EF , and the

**remaining**angles to the**remaining**angles : • the angleABC is therefore equal to the angle DEF : and the right angle ABK is equal to the

right angle DEN , whence the

**remaining**angle CBK is equal to the**remaining**...### 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.