Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 sider |
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Resultat 1-5 av 35
Side 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 ...
Side 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 ...
Side 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 angles 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 angles ABC , ABE , are equal to two right angles ( a ) : but the angles ABC , ABD , are ...
Side 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 ...
Side 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 B AC ...
... 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 B AC ...
Andre utgaver - Vis alle
Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... Dennis M'Curdy Uten tilgangsbegrensning - 1846 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Side 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.
Side 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.
Side 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.
Side 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.