Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 51
... inscribed in a circle ( ABCD ) are together equal to two right angles . In the quadrilateral figure ABCD , the two angles ABC , ADC are equal to two right angles : join AC and BD . In the triangle ABC , the three angles are equal to two ...
... inscribed in a circle ( ABCD ) are together equal to two right angles . In the quadrilateral figure ABCD , the two angles ABC , ADC are equal to two right angles : join AC and BD . In the triangle ABC , the three angles are equal to two ...
Σελίδα 55
... inscribed in a circle , any two of its opposite angles are equal to two right angles ( c ) ; there- fore , since ABC proves to be acute , its opposite ADC is obtuse , and it is in the less segment . Wherefore , in a circle , the angle ...
... inscribed in a circle , any two of its opposite angles are equal to two right angles ( c ) ; there- fore , since ABC proves to be acute , its opposite ADC is obtuse , and it is in the less segment . Wherefore , in a circle , the angle ...
Σελίδα 60
... inscribed in another , when all the angles of the former are upon the sides of the latter . Note . - Regular polygons , which have the same number of equal sides , thus inscribed , form a series , and have a certain ratio to each other ...
... inscribed in another , when all the angles of the former are upon the sides of the latter . Note . - Regular polygons , which have the same number of equal sides , thus inscribed , form a series , and have a certain ratio to each other ...
Σελίδα 61
... inscribe a triangle equiangular to a given triangle ( DEF ) . Construction . Draw the tangent GAH ( a ) ; at A , the ... inscribed in the given circle ABC , which was to be done . Recite ( a ) p . 17 , 3 ; ( d ) ax . 1 ; ( b ) 23 , 1 ...
... inscribe a triangle equiangular to a given triangle ( DEF ) . Construction . Draw the tangent GAH ( a ) ; at A , the ... inscribed in the given circle ABC , which was to be done . Recite ( a ) p . 17 , 3 ; ( d ) ax . 1 ; ( b ) 23 , 1 ...
Σελίδα 62
... inscribe a circle in a given triangle ( ABC ) . Constr . Bisect the angles B and C ( a ) , by straight lines BD , CD ... inscribed in the given triangle ( f ) ; which was to be done . Recite ( a ) p . 9 , 1 ; ( d ) ax . 10 ; ( b ) p . 12 ...
... inscribe a circle in a given triangle ( ABC ) . Constr . Bisect the angles B and C ( a ) , by straight lines BD , CD ... inscribed in the given triangle ( f ) ; which was to be done . Recite ( a ) p . 9 , 1 ; ( d ) ax . 10 ; ( b ) p . 12 ...
Άλλες εκδόσεις - Προβολή όλων
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD alternate angles angle ACD angles ABC angles equal antecedents Argument base BC bisected centre Chart chord circle ABC circumference Constr Denison Olmsted diameter draw drawn equal angles equal arcs equal radii equal sides equals the squares equi equiangular equilateral equilateral polygon equimultiples exterior angle fore Geometry given circle given rectilineal given straight line gles gnomon greater half inscribed isosceles isosceles triangle join less meet multiple opposite angles parallelogram parallelopipeds pentagon perimeter perpendicular plane polygon produced propositions Q. E. D. Recite radius ratio rectangle rectilineal figure School segment semicircle similar similar triangles sine square of AC tangent touches the circle triangle ABC unequal Wherefore
Δημοφιλή αποσπάσματα
Σελίδα 90 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα 117 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Σελίδα 92 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Σελίδα 79 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.
Σελίδα 87 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally...
Σελίδα 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 94 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Σελίδα 12 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Σελίδα 133 - If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.
Σελίδα 13 - AB be the greater, and from it cut (3. 1.) off DB equal to AC the less, and join DC ; therefore, because A in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides DB, BC are equal to the two AC, CB. each to each ; and the angle DBC is equal to the angle ACB; therefore the base DC is equal to the base AB, and the triangle DBC is< equal to the triangle (4. 1.) ACB, the less to 'the greater; which is absurd.