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 23
... ABD is a ftraight line , the angle DBE is equal to the angle EBA ; wherefore the angle DBE is equal to the angle CBE , the lefs to the greater ; which is impoffible ; therefore two straight lines cannot have a common segment .
... ABD is a ftraight line , the angle DBE is equal to the angle EBA ; wherefore the angle DBE is equal to the angle CBE , the lefs to the greater ; which is impoffible ; therefore two straight lines cannot have a common segment .
Side 26
AEB is equalb to the angle CEF , because they are oppofite vertical angles ; thereB E Α ' Let ABC be any triangle ; any two of its angles together are lefs than two right angles . Produce BC to D ; and because ACD is the exterior angle ...
AEB is equalb to the angle CEF , because they are oppofite vertical angles ; thereB E Α ' Let ABC be any triangle ; any two of its angles together are lefs than two right angles . Produce BC to D ; and because ACD is the exterior angle ...
Side 27
A For , if it be not greater , AC muft either be equal to AB , or less than it ; it is not equal , because then the angle ABC would be equal a to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it lefs ...
A For , if it be not greater , AC muft either be equal to AB , or less than it ; it is not equal , because then the angle ABC would be equal a to the angle ACB ; but it is not ; therefore AC is not equal to AB ; neither is it lefs ...
Side 28
Book I. ABC would be lefs b than the angle ACB ; but it is not ; there fore the fide AC is not lefs than AB ; and it has been fhewn b 18. I that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle ...
Book I. ABC would be lefs b than the angle ACB ; but it is not ; there fore the fide AC is not lefs than AB ; and it has been fhewn b 18. I that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle ...
Side 32
Book I. For , if it be not greater , it must either be equal to it , or lefs ; but the angle BAC is not equal to the angle EDF , because then the bafe BC would a 4. 1. be equal a to EF ; but it is not ; therefore the angle BAC is not ...
Book I. For , if it be not greater , it must either be equal to it , or lefs ; but the angle BAC is not equal to the angle EDF , because then the bafe BC would a 4. 1. be equal a to EF ; but it is not ; therefore the angle BAC is not ...
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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 |