## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical Trigonometry |

### Inni boken

Resultat 1-5 av 26

Side 101

If there be four magnitudes , and if any equimultiples whatsoever be taken of the

first and third , and any equimultiples whatsoever of the second and

, according as the multiple of the first is greater than the multiple of the second ...

If there be four magnitudes , and if any equimultiples whatsoever be taken of the

first and third , and any equimultiples whatsoever of the second and

**fourth**, and if, according as the multiple of the first is greater than the multiple of the second ...

Side 102

... first to the

the ratio of the second to the third , & c . “ So also , if there are five continual

proportionals ; the ratio of the first to the fifth is called quadruplicate of the ratio of

the ...

... first to the

**fourth**is said to be triplicate of the ratio of the first to the second , or ofthe ratio of the second to the third , & c . “ So also , if there are five continual

proportionals ; the ratio of the first to the fifth is called quadruplicate of the ratio of

the ...

Side 103

... is to the

of the second rank ; and so on in a cross , or inverse , order ; and the inference is

as in the 19th definition . It is demonstrated in the 23d Prop . of Book 5 . AXIOMS .

... is to the

**fourth**of the first rank , so is the third from the last , to the last but two ,of the second rank ; and so on in a cross , or inverse , order ; and the inference is

as in the 19th definition . It is demonstrated in the 23d Prop . of Book 5 . AXIOMS .

Side 105

If the first of four magnitudes has the same ratio to the second which the third has

to the

and any whatever of the second and

the ...

If the first of four magnitudes has the same ratio to the second which the third has

to the

**fourth**, and if any equimultiples whatever be taken of the first and third ,and any whatever of the second and

**fourth**; the multiple of the first · shall havethe ...

Side 106

If the first be the same multiple of the second , or the same part of it , that the third

is of the

be equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and ...

If the first be the same multiple of the second , or the same part of it , that the third

is of the

**fourth**; the first is to the second as the third to the**fourth**. First , if mA , mВbe equimultiples of the magnitudes A and B , mA : A :: mB : B. Take of mA and ...

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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities fall fore four fourth given given straight line greater half Hence inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism Prob produced PROP proportional proposition proved radius ratio reason rectangle contained rectilineal figure remaining right angles segment shewn sides similar sine solid square straight line taken tangent THEOR third touch triangle ABC wherefore whole