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 66
... A segment of a circle is the figure con- tained by a straight line and the circum- ference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and the circumference . " VIII . An angle in a ...
... A segment of a circle is the figure con- tained by a straight line and the circum- ference it cuts off . VII . " The angle of a segment is that which is contained by the straight line and the circumference . " VIII . An angle in a ...
Seite 67
... circle ABC . Which was to be found . A E B D COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . PROP . II . THEOR . IF ...
... circle ABC . Which was to be found . A E B D COR . From this it is manifest , that if in a circle a straight line bisect another at right angles , the centre of the circle is in the line which bisects the other . PROP . II . THEOR . IF ...
Seite 69
... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ... circle , & c . Q. E. D. E B C PROP . V. THEOR . IF two circles cut one another , they shall not have the same centre ...
... ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do not both pass ... circle , & c . Q. E. D. E B C PROP . V. THEOR . IF two circles cut one another , they shall not have the same centre ...
Seite 70
... circle ABC , CE is equal to EF : again , because E is the centre of the circle CDG , CE is equal to EG : but CE was shown to be equal to EF ; therefore EF is A / equal to EG , the less to the greater , which is impossible : therefore E ...
... circle ABC , CE is equal to EF : again , because E is the centre of the circle CDG , CE is equal to EG : but CE was shown to be equal to EF ; therefore EF is A / equal to EG , the less to the greater , which is impossible : therefore E ...
Seite 71
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
... ABCD be a circle , and AD its diameter , in which let any point F be taken which is not the centre ; let the centre be E ; of all the straight lines FB , FC , FG , & c . that can be drawn from F to the circumference , FA is the greatest ...
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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.