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 11
... which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI BOOK I. 11 THE ELEMENTS OF EUCLID .
... which coincide with one another , that is , which exactly fill the same space , are equal to one another . IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI BOOK I. 11 THE ELEMENTS OF EUCLID .
Seite 15
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF ...
... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the angle DEF ...
Seite 16
... whole AF is equal to the whole AG , of which the parts AB , AC , are equal : the remainder BF shall be equal ( 3. Ax . ) to the remain- der CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two ...
... whole AF is equal to the whole AG , of which the parts AB , AC , are equal : the remainder BF shall be equal ( 3. Ax . ) to the remain- der CG ; and FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two ...
Seite 35
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal ( 13 ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these equals add the angle ACB , and the angles ACD , ACB are equal to the three angles CBA , BAC , ACB ; but the angles ACD , ACB are equal ( 13 ...
Seite 37
... whole angle ABD is equal to the whole angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and an- gles of parallelograms are equal to one another ; also , their dia- meter bisects ...
... whole angle ABD is equal to the whole angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and an- gles of parallelograms are equal to one another ; also , their dia- meter bisects ...
Andere Ausgaben - Alle anzeigen
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.