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 13
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an ... ABC shall be an equilateral triangle . C A B E Because the point A is the centre of the circle BCD , AC is equal ( 15 ...
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an ... ABC shall be an equilateral triangle . C A B E Because the point A is the centre of the circle BCD , AC is equal ( 15 ...
Seite 15
... triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . B CE D F For , if the triangle ABC be ...
... triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . B CE D F For , if the triangle ABC be ...
Seite 16
... ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the ... triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of ...
... ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the ... triangle AFC to the triangle AGB ; and the remaining angles of the one are equal ( 4. 1. ) to the remaining angles of ...
Seite 18
... triangle ACB ; produce AC , AD to E , F ; there- fore , because AC is equal ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ... triangle ABC be applied to D G DEF , so that the point B B be on E , and the ...
... triangle ACB ; produce AC , AD to E , F ; there- fore , because AC is equal ... ABC , DEF be two triangles , having the two sides AB , AC , equal to the two ... triangle ABC be applied to D G DEF , so that the point B B be on E , and the ...
Seite 19
... triangles that have their sides which are terminated in one extremity of the base ... triangle DEF ; then join AF ; the straight line AF bisects the angle BAC ... ABC , and bi- sect ( 9. 1. ) the angle ACB by the straight line CD . AB is ...
... triangles that have their sides which are terminated in one extremity of the base ... triangle DEF ; then join AF ; the straight line AF bisects the angle BAC ... ABC , and bi- sect ( 9. 1. ) the angle ACB by the straight line CD . AB is ...
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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.