Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 sider |
Inni boken
Resultat 1-5 av 80
Side 32
... similar reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1. ) and DE is common ; therefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ; ( ax . 2 or 3. ) and AB is equal to DC ; ( 1. 24 ...
... similar reason , EF is equal to BC ; wherefore AD is equal to EF ; ( ax . 1. ) and DE is common ; therefore the whole , or the remainder AE , is equal to the whole , or the remainder DF ; ( ax . 2 or 3. ) and AB is equal to DC ; ( 1. 24 ...
Side 44
... similar distinction of triangles . Def . xxx - XXXIV . The definitions of quadrilateral figures are liable to objection . All of them , except the trapezium , fall under the general idea of a parallelogram ; but as Euclid defined ...
... similar distinction of triangles . Def . xxx - XXXIV . The definitions of quadrilateral figures are liable to objection . All of them , except the trapezium , fall under the general idea of a parallelogram ; but as Euclid defined ...
Side 49
... similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the ...
... similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the ...
Side 51
... similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . III . This problem admits of two solutions , and it is left unde- termined ...
... similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . III . This problem admits of two solutions , and it is left unde- termined ...
Side 55
... similar way , it may be shewn that BC cannot be otherwise than equal to EF . If ACB , DFE be both right angles : the case falls under Euc . 1. 26 . Prop . xxvII . Alternate angles are defined to be the two angles which two straight ...
... similar way , it may be shewn that BC cannot be otherwise than equal to EF . If ACB , DFE be both right angles : the case falls under Euc . 1. 26 . Prop . xxvII . Alternate angles are defined to be the two angles which two straight ...
Andre utgaver - Vis alle
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... Robert Potts Uten tilgangsbegrensning - 1845 |
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ... Euclid,Robert Potts Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Populære avsnitt
Side 54 - If two triangles have two sides of the one equal to two sides of the...
Side 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Side 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 18 - Any two angles of a triangle are together less than two right angles.
Side 266 - 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.
Side 152 - 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.
Side 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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...