The Elements of Euclid for the Use of Schools and CollegesMacmillan, 1872 - 400 sider |
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Side ix
... difference in the size of the pages . It will be perceived then , that in the present edition each distinct assertion in the argument begins a new line ; and at the ends of the lines are placed the necessary refer- ences to the ...
... difference in the size of the pages . It will be perceived then , that in the present edition each distinct assertion in the argument begins a new line ; and at the ends of the lines are placed the necessary refer- ences to the ...
Side 57
... difference of the squares on two unequal straight lines AC , CD , is equal to the rectangle contained by their sum and difference . PROPOSITION 6 . THEOREM . If a straight line be BOOK II . 5 . 57.
... difference of the squares on two unequal straight lines AC , CD , is equal to the rectangle contained by their sum and difference . PROPOSITION 6 . THEOREM . If a straight line be BOOK II . 5 . 57.
Side 133
... difference , the arc BC , contains two of the same parts . Bisect the arc BC at E ; [ III . 30 . therefore each of the arcs BE , EC is the fifteenth part of the whole circumference ABCDF . Therefore if the straight lines BE , EC be ...
... difference , the arc BC , contains two of the same parts . Bisect the arc BC at E ; [ III . 30 . therefore each of the arcs BE , EC is the fifteenth part of the whole circumference ABCDF . Therefore if the straight lines BE , EC be ...
Side 269
... difference of two straight lines is equal to the difference of the squares described on those straight lines ; or thus , the rectangle contained by two straight lines together with the square described on half their difference , is ...
... difference of two straight lines is equal to the difference of the squares described on those straight lines ; or thus , the rectangle contained by two straight lines together with the square described on half their difference , is ...
Side 275
... of B and C double of D ; then in the first part it is assumed that the sum of A and C is double of the sum of B and D , and in the second part it is as sumed that the difference of A and C is double 18-2 EUCLID'S ELEMENTS . 275.
... of B and C double of D ; then in the first part it is assumed that the sum of A and C is double of the sum of B and D , and in the second part it is as sumed that the difference of A and C is double 18-2 EUCLID'S ELEMENTS . 275.
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Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore