## 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 119

Geometers make use of the following technical words to signify certain ways of

changing either the order or magnitude of

still to be

Geometers make use of the following technical words to signify certain ways of

changing either the order or magnitude of

**proportionals**, so as that they continuestill to be

**proportionals**. XIII . Permutando , or alternando , by permutation , or ... Side 171

1 lar : but the sides about the equal angles of equal parallelograms are

reciprocally

rectangle contained by the extremes is equal to the square of the mean : and if

the rectangle ...

1 lar : but the sides about the equal angles of equal parallelograms are

reciprocally

**proportional**( 14. 6. ) ... IF three straight lines be**proportionals**, therectangle contained by the extremes is equal to the square of the mean : and if

the rectangle ...

Side 177

Let each of the rectilineal figures , A , B be similar to the rectilineal figure C ; the

figure A is similar to the figure B. Because A is similar to C ; they are equiangular ,

and also have their sides about the equal angles

Let each of the rectilineal figures , A , B be similar to the rectilineal figure C ; the

figure A is similar to the figure B. Because A is similar to C ; they are equiangular ,

and also have their sides about the equal angles

**proportionals**( 1 def . 6. ) . Side 245

If four straight lines be

described from them shall also be

parallelopipeds similarİy described from four straight lines be

straight lines ...

If four straight lines be

**proportionals**, the similar solid parallelopipeds similarlydescribed from them shall also be

**proportionals**. And if the similarparallelopipeds similarİy described from four straight lines be

**proportionals**, thestraight lines ...

Side 313

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

F , H be

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

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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.