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 35.
Σελίδα 15
... Argument . AC is made equal to BC , the angle ACD to BCD , and CD is common to the two tri- angles ACD , BCD : therefore , the bases AD and BD are equal , and AB is cut into two equal parts in the point D. Which was to be done . Recite ...
... Argument . AC is made equal to BC , the angle ACD to BCD , and CD is common to the two tri- angles ACD , BCD : therefore , the bases AD and BD are equal , and AB is cut into two equal parts in the point D. Which was to be done . Recite ...
Σελίδα 16
... Argument . The triangles CHF , CHG have CH common , HF equal to HG , and the bases CF , CG are equal radii ; there- fore , the angles CHF , CHG , are equal ( d ) , and being adjacent , they are right angles ( e ) , and CH drawn from the ...
... Argument . The triangles CHF , CHG have CH common , HF equal to HG , and the bases CF , CG are equal radii ; there- fore , the angles CHF , CHG , are equal ( d ) , and being adjacent , they are right angles ( e ) , and CH drawn from the ...
Σελίδα 17
... Argument . If CBD be not a straight line , make CBE such : therefore , since AB makes angles with the straight line CBE , on one side of it , the augles ABC , ABE , are equal to two right angles ( a ) : but the angles ABC , ABD , are ...
... Argument . If CBD be not a straight line , make CBE such : therefore , since AB makes angles with the straight line CBE , on one side of it , the augles ABC , ABE , are equal to two right angles ( a ) : but the angles ABC , ABD , are ...
Σελίδα 18
... Argument . Produce the side BC to D ( a ) . Then since the interior angle B is less than the exterior and opposite angle ACD ( b ) , to each add ACB ; then ACB and B are less than ACB and ACD ( c ) : but these latter two are equal to ...
... Argument . Produce the side BC to D ( a ) . Then since the interior angle B is less than the exterior and opposite angle ACD ( b ) , to each add ACB ; then ACB and B are less than ACB and ACD ( c ) : but these latter two are equal to ...
Σελίδα 19
... Argument . The angles ACD , ADC are equal , being opposite to equal sides ( a ) ; but either of them is less than BCD ; and the less side subtends the less angle ( b ) ; therefore BC is less than BD , which is the sum of BA and AC . B C ...
... Argument . The angles ACD , ADC are equal , being opposite to equal sides ( a ) ; but either of them is less than BCD ; and the less side subtends the less angle ( b ) ; therefore BC is less than BD , which is the sum of BA and AC . B C ...
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 Q. E. D. Recite radius ratio rectangle rectangle contained 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 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.
Σελίδα 71 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall...
Σελίδα 83 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words