## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 5

Side 476

OF

geometrical progression , proceeding from l , are also called the

numbers in that series * . Thus , if a denote any number , and the geometrical

series ...

OF

**LOGARITHMS**. : 1. The indices or exponents of a series of numbers ingeometrical progression , proceeding from l , are also called the

**logarithms**of thenumbers in that series * . Thus , if a denote any number , and the geometrical

series ...

Side 478

Continuing the advancement of the powers of 1 + a , the numbers 3 , 4 , 5 , & c . ,

for the same reasons , will fall into the series . 6. The sum of the

two numbers is equal to the

Continuing the advancement of the powers of 1 + a , the numbers 3 , 4 , 5 , & c . ,

for the same reasons , will fall into the series . 6. The sum of the

**logarithms**of anytwo numbers is equal to the

**logarithm**of the product of the same two numbers . Side 482

Consequently the hyperbolic

0.11778303566 = 0.69314718054 . The hyperbolic

found , that of 4 , 8 , 16 , and all the other powers of 2 may be obtained by

multiplying the ...

Consequently the hyperbolic

**logarithm**of the number 2 is 0.57536414488 +0.11778303566 = 0.69314718054 . The hyperbolic

**logarithm**of 2 being thusfound , that of 4 , 8 , 16 , and all the other powers of 2 may be obtained by

multiplying the ...

Side 486

т т т 4 m 6 : : 1 : m therefore 1 , 21 , 31 , & c . be hyperbolic

by the methods already explained , the

be derived from them ; for the hyperbolic

т т т 4 m 6 : : 1 : m therefore 1 , 21 , 31 , & c . be hyperbolic

**logarithms**, calculatedby the methods already explained , the

**logarithms**expressed by 1 2,3 , & c . maybe derived from them ; for the hyperbolic

**logarithm**of any given number is to ... Side 487

1 from 1 , the common

5. Hence the common

common

the ...

1 from 1 , the common

**logarithm**of 10 ; for 10 being divided by 2 , the quotient is5. Hence the common

**logarithm**of 5 is 0.6989700044 . Again , to find thecommon

**logarithm**of 3 , 2.30258509324 : 1 :: 1.0986122 8864 : 0.4771212546the ...

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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Side 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.

Side 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...

Side 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.

Side 97 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.