Euclid's Elements of geometry, the first four books, by R. Potts. Corrected and improved1864 |
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Σελίδα 46
... converse , should both be of such a nature as that neither of them should require a formal demonstration . The first and most simple idea , derived from experience is , that every magnitude fills a certain space , and that several ...
... converse , should both be of such a nature as that neither of them should require a formal demonstration . The first and most simple idea , derived from experience is , that every magnitude fills a certain space , and that several ...
Σελίδα 51
... converse of one part of Prop . v . One proposition " is defined to be the converse of another when D 2 NOTES TO BOOK I. 51.
... converse of one part of Prop . v . One proposition " is defined to be the converse of another when D 2 NOTES TO BOOK I. 51.
Σελίδα 52
... converse . In this manner , Prop . VIII . is the converse of Prop . IV . It may here be observed , that converse theorems are not universally true : as for instance , the following direct proposition is universally true ; “ If two ...
... converse . In this manner , Prop . VIII . is the converse of Prop . IV . It may here be observed , that converse theorems are not universally true : as for instance , the following direct proposition is universally true ; “ If two ...
Σελίδα 53
... converse of Prop . xIII . " Upon the opposite sides of it . " If these words were omitted , it is possible for two lines to make with a third , two angles , which together are equal to two right angles , in such a manner that the two ...
... converse of Prop . xIII . " Upon the opposite sides of it . " If these words were omitted , it is possible for two lines to make with a third , two angles , which together are equal to two right angles , in such a manner that the two ...
Σελίδα 55
... converse of it forms Euc . 1. 17 ; for both the assumed axiom and its converse , should be so obvious as not to require formal demonstration . Simson has attempted to overcome the objection , not by any improved definition and axiom ...
... converse of it forms Euc . 1. 17 ; for both the assumed axiom and its converse , should be so obvious as not to require formal demonstration . Simson has attempted to overcome the objection , not by any improved definition and axiom ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements of Geometry, the First Four Books, by R. Potts. Corrected ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ... Euclides Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1864 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.