Euclid's Elements of geometry, the first four books, by R. Potts. Corrected and improved1864 |
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Seite 5
... sides equal , but its angles are not right angles . XXXIII . A rhomboid has its opposite sides equal to each other , but all its sides are not equal , nor its angles right angles . XXXIV . All other four - sided figures besides these ...
... sides equal , but its angles are not right angles . XXXIII . A rhomboid has its opposite sides equal to each other , but all its sides are not equal , nor its angles right angles . XXXIV . All other four - sided figures besides these ...
Seite 8
... sides are opposite . Let ABC , DEF be two triangles , which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF , and the included angle BAC equal to the included angle EDF . Then ...
... sides are opposite . Let ABC , DEF be two triangles , which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF , and the included angle BAC equal to the included angle EDF . Then ...
Seite 9
... sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . A D B C E F For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and ...
... sides are opposite shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . A D B C E F For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and ...
Seite 10
... sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB . And because the whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; therefore the remainder BF is equal to the ...
... sides are opposite ; viz . the angle ACF to the angle ABG , and the angle AFC to the angle AGB . And because the whole AF is equal to the whole AG , of which the parts AB , AC , are equal ; therefore the remainder BF is equal to the ...
Seite 16
... opposite sides of it , make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD ...
... opposite sides of it , make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD ...
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Euclid's Elements of Geometry, the First Four Books, by R. Potts. Corrected ... Euclides Keine Leseprobe verfügbar - 2016 |
Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ... Euclides Keine Leseprobe verfügbar - 1864 |
Häufige Begriffe und Wortgruppen
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal Apply Euc axiom base BC bisecting the angle chord circle ABC circumference construction demonstrated describe a circle diagonals diameter double draw equal angles equal to twice equiangular equilateral triangle Euclid Euclid's Elements exterior angle Geometry given angle given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle Let ABC line AC line CD line joining lines be drawn meet the circumference opposite angles opposite sides parallel parallelogram pentagon perpendicular porism problem produced Prop proved quadrilateral figure radius rectangle contained remaining angle right angles right-angled triangle segment semicircle shew shewn side BC square on AC tangent THEOREM touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
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Seite 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Seite 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Seite 30 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 54 - If two triangles have two sides of the one equal to two sides of the...
Seite 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 85 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Seite 41 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Seite 126 - EF, that is, AF, is greater than BF : Again, because BE is equal to CE, and FE common to the triangles BEF, CEF, the two sides BE, EF are equal to the two CE, EF; but the angle BEF is greater than the angle CEF ; therefore the base BF is greater (24. 1.) than the base FC ; for the same reason, CF is greater than GF. Again, because GF, FE are greater (20.