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 14
... equal to DG , and DA , DB , parts of them , are equal therefore the remainder AL is equal to the remain- der ( 3. Ax . ) BG ; but it has been shown , that BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things ...
... equal to DG , and DA , DB , parts of them , are equal therefore the remainder AL is equal to the remain- der ( 3. Ax . ) BG ; but it has been shown , that BC is equal to G , wherefore AL and BC are each of them equal to BG ; and things ...
Seite 15
... equal to the angle EDF , the base BC shall be equal to the base EF ; and the 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 ...
... equal to the angle EDF , the base BC shall be equal to the base EF ; and the 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 ...
Seite 16
... equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to AC , the two sides ...
... equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off AG equal ( 3. 1. ) to AF , the less , and join FC , GB . Because AF is equal to AG , and AB to AC , the two sides ...
Seite 17
... equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
... equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
Seite 18
... equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ...
... equal to AD in the E F triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ...
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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.