Euclid's Elements of geometry, the first four books, by R. Potts. Corrected and improved1864 |
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Αποτελέσματα 6 - 10 από τα 90.
Σελίδα 17
... angles made by any num- ber of lines meeting in one point , are together equal to four right angles . PROPOSITION XVI . THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite ...
... angles made by any num- ber of lines meeting in one point , are together equal to four right angles . PROPOSITION XVI . THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite ...
Σελίδα 18
... opposite vertical angles ; ( I. 15. ) therefore the base AB is equal to the base CF , ( 1. 4. ) and the triangle AEB ... sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD or ACD is greater than ...
... opposite vertical angles ; ( I. 15. ) therefore the base AB is equal to the base CF , ( 1. 4. ) and the triangle AEB ... sides are opposite ; wherefore the angle BAE is equal to the angle ECF ; but the angle ECD or ACD is greater than ...
Σελίδα 19
... opposite angle DCB ; ( 1. 16. ) but the angle ADB has been proved equal to the angle ABD , therefore the angle ABD ... sides of a triangle are together greater than the third side . Let ABC be a triangle . Then any two sides of it ...
... opposite angle DCB ; ( 1. 16. ) but the angle ADB has been proved equal to the angle ABD , therefore the angle ABD ... sides of a triangle are together greater than the third side . Let ABC be a triangle . Then any two sides of it ...
Σελίδα 21
... opposite angle ; ( 1. 16. ) therefore the exterior angle BDC of the triangle ... sides shall be equal to three given straight lines , but any two whatever of ... sides shall be equal to A , B , C , each to each . A. B. C- K D G H E L Take ...
... opposite angle ; ( 1. 16. ) therefore the exterior angle BDC of the triangle ... sides shall be equal to three given straight lines , but any two whatever of ... sides shall be equal to A , B , C , each to each . A. B. C- K D G H E L Take ...
Σελίδα 24
... angles of the other , each to each , and one side equal to one side , viz . either the sides adja- cent to the equal angles in each , or the sides opposite to them ; then shall the other sides be equal , each to each , and also the ...
... angles of the other , each to each , and one side equal to one side , viz . either the sides adja- cent to the equal angles in each , or the sides opposite to them ; then shall the other sides be equal , each to each , and also the ...
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.