Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations in Euclid, part ii., with illustr. [&c.] by H. Green1861 |
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Página 163
... Arith . Hyp . - Let A = 24 , B say m times , or 3 , of a = 21 , C = 18 , & c . , be equimults . 8 , b = 7 , & c = = 6 . mb = b + b + b ; - Alg . Then . * A = ma = a + a + a ; B & C = mcc + c + c ; the Equals , A + B + C = ma + mb + mc ...
... Arith . Hyp . - Let A = 24 , B say m times , or 3 , of a = 21 , C = 18 , & c . , be equimults . 8 , b = 7 , & c = = 6 . mb = b + b + b ; - Alg . Then . * A = ma = a + a + a ; B & C = mcc + c + c ; the Equals , A + B + C = ma + mb + mc ...
Página 165
... Arith . Hyp . - Take 6 quantities A 16 , F. 14 , m = = 3 , and n = 2 . = Alg . Arith . - L F 24 , B8 , C = 21 , D = 7 , A the 1st m B , and C the 3rd m D. E the 5th n B , and F the 6th = nD ; + equals , then A + E ( m + n ) B and C + F ...
... Arith . Hyp . - Take 6 quantities A 16 , F. 14 , m = = 3 , and n = 2 . = Alg . Arith . - L F 24 , B8 , C = 21 , D = 7 , A the 1st m B , and C the 3rd m D. E the 5th n B , and F the 6th = nD ; + equals , then A + E ( m + n ) B and C + F ...
Página 166
... Arith . Hyp . — Take a → 12 , 64 , c Alg . - Let a mb , and c md ; then na 15 , d5 ; m → 3 & n — 2 . mnb , and ne →→ mnd ; i . e . , the equims . na & nc of the 1st and 3rd , are mults . of the 2nd and 4th . Arith . 12 = 3 × 4 , and ...
... Arith . Hyp . — Take a → 12 , 64 , c Alg . - Let a mb , and c md ; then na 15 , d5 ; m → 3 & n — 2 . mnb , and ne →→ mnd ; i . e . , the equims . na & nc of the 1st and 3rd , are mults . of the 2nd and 4th . Arith . 12 = 3 × 4 , and ...
Página 167
Euclides Henry Green. Arith . 12 = 3 × 4 , and 15 = 3 × 5 , .. 2 × 12 = 6 × 4 , & 2 × 15 = 6 X 5 ; i . e . the equims . 24 & 30 , of the 1st 12 , and 3rd 15 , are equims . of the 2nd 4 , and of the 4th 5 . SCH . " If any equimultiples m ...
Euclides Henry Green. Arith . 12 = 3 × 4 , and 15 = 3 × 5 , .. 2 × 12 = 6 × 4 , & 2 × 15 = 6 X 5 ; i . e . the equims . 24 & 30 , of the 1st 12 , and 3rd 15 , are equims . of the 2nd 4 , and of the 4th 5 . SCH . " If any equimultiples m ...
Página 169
... Arith . Hyp . - Let a 2 , b ≈ 5 , c = 4 , d = 10 , m = 2 & n = 3 . Alg . - a : b cd , then ma : nb = mc : nd . For , 3 , V. equims . of ma and me are equims . of a & c ; and equims of nb , nd also equims . of b & d . But , Def . 5 , V ...
... Arith . Hyp . - Let a 2 , b ≈ 5 , c = 4 , d = 10 , m = 2 & n = 3 . Alg . - a : b cd , then ma : nb = mc : nd . For , 3 , V. equims . of ma and me are equims . of a & c ; and equims of nb , nd also equims . of b & d . But , Def . 5 , V ...
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Euclid's Plane Geometry, Books III.-VI., Practically Applied; Or, Gradations ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD Antecs Arith base bisected centre chord circumference circumscribed compd Conc contained decagon desc diam diameter distance divided draw drawn equiangular equims equimultiples Euclid extreme four magnitudes fourth Geometry given circle given line given st greater hypotenuse inscribed isosc join less mean measure multiple parallel parallelogram pentagon perp Plane Geometry polygon PROB Prop propl proportional proposition Quæs radius ratio compounded rect rectangle rectil rectilineal figure regular polygon Remk segments semic semiperimeter sides similar square star-shaped polygon straight line tang tangent third touch triangle vertex
Pasajes populares
Página 7 - If two triangles have two sides of the one equal to two sides of the...
Página 151 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any...
Página 81 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 85 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Página 310 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 11 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Página 33 - The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Página 156 - XIII. Permutando, or alternando, by permutation, or alternately; this word is used when there are four proportionals, and it is inferred, that the first has the same ratio to the third, which the second has to the ,fourth; or that the first is to the third, as the second to the fourth; as is shown in the 16th prop.
Página 219 - If there be any number of magnitudes, and as many others, which, taken two and two in 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 "ex sequali,
Página 216 - 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