## 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 |

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Side vi

that no definition , except that of Euclid , has ever been given , from which the properties of

that no definition , except that of Euclid , has ever been given , from which the properties of

**proportionals**can be deduced by reasonings , which , at the same time that they are perfectly rigorous , are also simple and direct . Side 108

Magnitudes are said to be

Magnitudes are said to be

**proportionals**, when the first has the same ratio to the second that the third has to the fourth ; and the third to the fourth the same ratio which the fifth has to the sixth , and so on whatever be their ... Side 109

When three magnitudes are continual

When three magnitudes are continual

**proportionals**, the second is said to be a mean**proportional**between the other two . X. When there is any number of magnitudes of the same kind , the first is said to have to the last the ratio ... Side 110

If four magnitudes are continual

If four magnitudes are continual

**proportionals**, the ratio of the first to the fourth is said to be triplicate of the ratio of the first to the second , or of the ratio of the second to the third , & c . " So also , if there are five ... Side 111

Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when e there is any number of magnitudes more than two , and as many others , so that they are

Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when e there is any number of magnitudes more than two , and as many others , so that they are

**proportionals**when taken two and two of each rank , and it is ...### Hva folk mener - Skriv en omtale

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |

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 - 1855 |

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