Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ...Collins, Brother & Company, 1846 - 138 páginas |
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Página 25
... excess ; and if less , DE will be a common segment of AD , EF . To each , there- fore , add the excess , or from each subtract the segment ; the sums , or differences , AE , DF , will be equal ( d ) . In either case , therefore , the ...
... excess ; and if less , DE will be a common segment of AD , EF . To each , there- fore , add the excess , or from each subtract the segment ; the sums , or differences , AE , DF , will be equal ( d ) . In either case , therefore , the ...
Página 81
... excess above the second as the third is to its excess above the fourth . Given AB BE :: CD : DF ; then , by hyp . , AB : AB - BE :: CD : CD - DF . Let the parts of AB be AE , EB , and the parts of CD be CF , FD . Then , since AB : EB ...
... excess above the second as the third is to its excess above the fourth . Given AB BE :: CD : DF ; then , by hyp . , AB : AB - BE :: CD : CD - DF . Let the parts of AB be AE , EB , and the parts of CD be CF , FD . Then , since AB : EB ...
Página 102
... excess is BG . M . 27 Th . The greatest of all defective parallelograms applied to the same straight line , is that described upon its half ; provided each of the defects be similar to the paral- lelogram described upon half the line ...
... excess is BG . M . 27 Th . The greatest of all defective parallelograms applied to the same straight line , is that described upon its half ; provided each of the defects be similar to the paral- lelogram described upon half the line ...
Página 103
... excess of EF above CC , and similar to D , or EF ( d ) ; and let EG be homolo- gous to KL , and GF to LM . Therefore EF , being equal to KM and CC both , is greater than KM ; and its sides EG , GF exceed the sides KL , LM . Make GX ...
... excess of EF above CC , and similar to D , or EF ( d ) ; and let EG be homolo- gous to KL , and GF to LM . Therefore EF , being equal to KM and CC both , is greater than KM ; and its sides EG , GF exceed the sides KL , LM . Make GX ...
Página 104
... excess OP similar to EL , since they are about the same diame- ter ( h ) ; and EL is similar to D ; wherefore OP is also similar to D , as required . Therefore to a given straight line is applied , & c . , which was to be done . Recite ...
... excess OP similar to EL , since they are about the same diame- ter ( h ) ; and EL is similar to D ; wherefore OP is also similar to D , as required . Therefore to a given straight line is applied , & c . , which was to be done . Recite ...
Otras ediciones - Ver todas
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Sin vista previa disponible - 2017 |
Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Sin vista previa disponible - 2017 |
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 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.
Página 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.
Página 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...
Página 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