## 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 8

Side 295

BOOK I. N It is necessary to consider a solid , that is , a

length , breadth , and thickness , in order to understand aright the definitions of a

point , line , and superficies ; for these all arise from a solid , and exist in it : the ...

BOOK I. N It is necessary to consider a solid , that is , a

**magnitude**which haslength , breadth , and thickness , in order to understand aright the definitions of a

point , line , and superficies ; for these all arise from a solid , and exist in it : the ...

Side 313

this book : the author of it designed to demonstrate , that if four

F , H be proportionals , they are also proportionals inversely , that is , G is to E , as

H to F ; which is true ; but the demonstration of it does not in the least depend ...

this book : the author of it designed to demonstrate , that if four

**magnitudes**E , G ,F , H be proportionals , they are also proportionals inversely , that is , G is to E , as

H to F ; which is true ; but the demonstration of it does not in the least depend ...

Side 365

I. SPACEs , lines , and angles , are said to be given in

to them can be found . II . A ratio is said to be given , when a ratio of a given

I. SPACEs , lines , and angles , are said to be given in

**magnitude**, when equalsto them can be found . II . A ratio is said to be given , when a ratio of a given

**magnitude**to a given**magnitude**which is the same ratio with it can be found . III . Side 366

X. A

given

1 . PROPOSITION I. The ratios of given

...

X. A

**magnitude**is said to be less than another by a given**magnitude**, when thisgiven

**magnitude**being added to it , the whole is equal to the other**magnitude**. *1 . PROPOSITION I. The ratios of given

**magnitudes**to one another are given.t Let...

Side 373

A. If a

given ratio to the first

...

A. If a

**magnitude**together with a given**magnitude**has a given ratio to another**magnitude**; the excess of this other**magnitude**above a given**magnitude**has agiven ratio to the first

**magnitude**: and if the excess of a**magnitude**above a given...

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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.