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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Σελίδα 6
... expects twenty to one of the same kind . By the same rule , therefore , we may have twenty Euclids to one from the Common Schools and Academies . New York , March , 1846 . SECOND LESSONS IN GEOMETRY . BOOK I. Definitions . 1. 6 PREFACE .
... expects twenty to one of the same kind . By the same rule , therefore , we may have twenty Euclids to one from the Common Schools and Academies . New York , March , 1846 . SECOND LESSONS IN GEOMETRY . BOOK I. Definitions . 1. 6 PREFACE .
Σελίδα 7
... common segment ; but , meeting in two points , or coinci- ding in part , they shall coincide in all their length . Note . Straight lines have certain relations to one another from their position ; namely , perpendicular , meeting ...
... common segment ; but , meeting in two points , or coinci- ding in part , they shall coincide in all their length . Note . Straight lines have certain relations to one another from their position ; namely , perpendicular , meeting ...
Σελίδα 13
... common to both : there- fore the bases , BG and CF , are equal , and like- wise the angles ABG , ACF ; as also the angles at F , G ( d ) . F The two triangles BCG , CBF , are also equal : for it is shown above , that FC , FB , and the ...
... common to both : there- fore the bases , BG and CF , are equal , and like- wise the angles ABG , ACF ; as also the angles at F , G ( d ) . F The two triangles BCG , CBF , are also equal : for it is shown above , that FC , FB , and the ...
Σελίδα 15
... common to the two triangles DAF , EAF , and the bases DF , EF , were made equal : there- fore the angle DAF is equal to EAF ( d ) ; that is , the rectilineal angle BAC is bisected by the straight line AF ; which was to be done . D ...
... common to the two triangles DAF , EAF , and the bases DF , EF , were made equal : there- fore the angle DAF is equal to EAF ( d ) ; that is , the rectilineal angle BAC is bisected by the straight line AF ; which was to be done . D ...
Σελίδα 16
... common segment : for if ABC , ABD , have the segment AB common , they cannot both be straight lines . Draw BE at right angles to AB ( a ) then if ABC be a straight line , EBC is a right angle ; and if ABD be a straight line , EBD is a ...
... common segment : for if ABC , ABD , have the segment AB common , they cannot both be straight lines . Draw BE at right angles to AB ( a ) then if ABC be a straight line , EBC is a right angle ; and if ABD be a straight line , EBD is a ...
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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.