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 CorrectedDesilver, 1829 - 516 Seiten |
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Seite 3
... Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppress- ing others , and mixing his own with Euclid's Demonstra- tions , had changed more things to the ...
... Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppress- ing others , and mixing his own with Euclid's Demonstra- tions , had changed more things to the ...
Seite 80
... Greek text and translations from it , the angle of the semicircle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . ' COR . From this it is manifest , that the straight ...
... Greek text and translations from it , the angle of the semicircle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . ' COR . From this it is manifest , that the straight ...
Seite 91
... the cir- cumference of the less segment ADC falls within the right an- gle CAF . " And this is all that is meant , when in the Greek text , and the translations from it , the angle. BOOK III . 91 THE ELEMENTS OF EUCLID .
... the cir- cumference of the less segment ADC falls within the right an- gle CAF . " And this is all that is meant , when in the Greek text , and the translations from it , the angle. BOOK III . 91 THE ELEMENTS OF EUCLID .
Seite 271
... Greek , because the pyra- mid , in what follows , is supposed to be circumscribed about the cone , and so must have the same vertex . And the same change is made in some places following . ( Lem . 1. ) than the solid Z : BOOK XII . 271 ...
... Greek , because the pyra- mid , in what follows , is supposed to be circumscribed about the cone , and so must have the same vertex . And the same change is made in some places following . ( Lem . 1. ) than the solid Z : BOOK XII . 271 ...
Seite 291
... GREEK TEXT ; AND THE REASONS OF THE ALTERATIONS WHICH HAVE BEEN MADE . AS ALSO OBSERVATIONS ON SOME OF THE PROPOSITIONS . BY ROBERT SIMSON , M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW . NOTES , CRITICAL AND ...
... GREEK TEXT ; AND THE REASONS OF THE ALTERATIONS WHICH HAVE BEEN MADE . AS ALSO OBSERVATIONS ON SOME OF THE PROPOSITIONS . BY ROBERT SIMSON , M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW . NOTES , CRITICAL AND ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Beliebte Passagen
Seite 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 81 - The angles in the same segment of a circle are equal to one another.
Seite 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Seite 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Seite 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 22 - ANY two angles of a triangle are together less than two right angles.
Seite 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Seite 24 - Any two sides of a triangle are together greater than the third side.