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 Restored : Also the Book of Euclid's Data, in Like Manner CorrectedJ. Nourse, London, 1781 - 520 sider |
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Side 6
... Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and not affumed ; and , therefore , though this were a true Propo- fition , it ought to have been ...
... Magnitude . " Now , this Propofition is a Theorem , not a Definition ; because the equality of Figures of any kind must be demonftrated , and not affumed ; and , therefore , though this were a true Propo- fition , it ought to have been ...
Side 119
... magnitude is faid to be a part of a greater magni- tude , when the lefs measures the greater , that is , when the lefs is contained a certain number of times exactly in the greater . ' II . A greater magnitude is faid to be a multiple ...
... magnitude is faid to be a part of a greater magni- tude , when the lefs measures the greater , that is , when the lefs is contained a certain number of times exactly in the greater . ' II . A greater magnitude is faid to be a multiple ...
Side 120
... Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is ... magnitude . For example , If A , B , C , D be four magnitudes of the fame kind , the first A is said to have to the ...
... Magnitudes which have the fame ratio are called proportionals , N. B. When four magnitudes are proportionals , it is ... magnitude . For example , If A , B , C , D be four magnitudes of the fame kind , the first A is said to have to the ...
Side 122
... magnitudes are taken two and two . ' XIX . Ex aequali , from equality ; this term is ufed fimply by itself , when the firft magnitude is to the fecond of the first rank , as the firft to the fecond of the other rank ; and as the fe ...
... magnitudes are taken two and two . ' XIX . Ex aequali , from equality ; this term is ufed fimply by itself , when the firft magnitude is to the fecond of the first rank , as the firft to the fecond of the other rank ; and as the fe ...
Side 123
... magnitude is greater than the fame multiple of a less . IV . That magnitude of which a multiple is greater than the fame multiple of another , is greater than that other magnitude . IF PROP . I. THEOR . any number of magnitudes be ...
... magnitude is greater than the fame multiple of a less . IV . That magnitude of which a multiple is greater than the fame multiple of another , is greater than that other magnitude . IF PROP . I. THEOR . any number of magnitudes be ...
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The Elements of Euclid: Viz. The First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1793 |
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alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle bifected Book XI cafe centre circle ABCD circumference cone confequently conftruction cylinder defcribed demonftrated diameter drawn equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fides BA fimilar fince firft firſt folid angle fome fore fphere fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC oppofite parallel parallelepipeds parallelogram perpendicular polygon prifm propofition proportionals pyramid Q. E. D. PROP rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC vertex wherefore