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 Corr |
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Side 120
Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ' ufually expreffed by faying , the first is to the fecond , as the third to the fourth . ' VII .
Magnitudes which have the fame ratio are called proportionals . N. B. When four magnitudes are proportionals , it is ' ufually expreffed by faying , the first is to the fecond , as the third to the fourth . ' VII .
Side 121
In proportionals , the antecedent terms are called homologous to one another , as alfo the confequents to one another . ' Geometers make ufe of the following technical words to fignify certain ways of changing either the order or magni' ...
In proportionals , the antecedent terms are called homologous to one another , as alfo the confequents to one another . ' Geometers make ufe of the following technical words to fignify certain ways of changing either the order or magni' ...
Side 129
... D F IF [ F four magnitudes are proportionals , they are propor- see N. tionals alfo when taken inversely . 3 Book V. is Fr a 5. def . § . f Book V. is to A , fo is D to OF EUCLID . 129.
... D F IF [ F four magnitudes are proportionals , they are propor- see N. tionals alfo when taken inversely . 3 Book V. is Fr a 5. def . § . f Book V. is to A , fo is D to OF EUCLID . 129.
Side 136
Wherefore , ratios that , & c . QE . D. G AB PROP . XII . THEOR . IF any number of magnitudes be proportionals , as one of the antecedents is to its confequent , fo fhall all the antecedents taken together be to all the confequents .
Wherefore , ratios that , & c . QE . D. G AB PROP . XII . THEOR . IF any number of magnitudes be proportionals , as one of the antecedents is to its confequent , fo fhall all the antecedents taken together be to all the confequents .
Side 139
Q , E. D. IF four magnitudes of the fame kind be proportionals they hail also be proportionals when taken alternately . Let the four magnitudes A , B , C , D be proportionals , viz . 25 A to B , fo C to D : They fhall alfo be ...
Q , E. D. IF four magnitudes of the fame kind be proportionals they hail also be proportionals when taken alternately . Let the four magnitudes A , B , C , D be proportionals , viz . 25 A to B , fo C to D : They fhall alfo be ...
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The Elements of Euclid: Viz the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1803 |
The Elements of Euclid, Viz; The First Six Books: Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
added alfo alſo altitude angle ABC angle BAC bafe baſe becauſe Book Book XI centre circle circle ABCD circumference common cone cylinder defcribed definition demonftrated diameter divided double draw drawn equal equal angles equiangular equimultiples fame fame multiple fecond fegment fhall fides fimilar firft firſt folid fore four fourth fquare fquare of BC ftraight line given angle given in fpecies given in pofition given magnitude given ratio given ſtraight line greater Greek half join lefs leſs magnitude manner meet oppofite parallel parallelogram perpendicular plane produced PROP propofition proportionals pyramid reaſon rectangle rectangle contained remaining right angles ſquare Take taken THEOR theſe third triangle ABC wherefore whole
Bibliografisk informasjon
| Tittel | 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 Corr |
| Forfatter | Euclid |
| Utgiver | E. Wingrove, London, and J. Balfour, Edinburgh, 1793 |
| Original fra | Harvard University |
| Digitalisert | 17. apr 2019 |
| Lengde | 520 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |