Mathematical recreations, containing solutions of many very difficult and important equations, and of several useful problems in geometry, surveying and astronomy, together with a method of finding roots and equations by projection — 数学遊戯

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Mathematical recreations, containing solutions of many verydifficult and important equations, and…

数式・計算（OCR転写）：From [1], we find f-Cf = (i-l)i

therefore i-l = (r-Q)i,原文 From [1], we find f-Cf = (i-l)i therefore i-l = (r-Q)i, B0021｜原版スキャンp.8…

数式・計算（OCR転写）：Hence ^ = 5 or --, 3/ = 3 or -^g原文 Hence ^ = 5 or --, 3/ = 3 or -^gB0086｜原版スキャンp.1…

数式・計算（OCR転写）：But -^x = I/; -^x = 4 or 1, x = 16

or 1.原文 But -^x = I/; -^x = 4 or 1, x = 16 or 1. B0107｜原版スキャンp.13／原版本文p.6｜原文順0107｜ロビンソン本文原版記号・OCR…

数式・計算（OCR転写）：10— lOiz+lOy^-lOy'+lO)/'' =

Uy+Uy'; 10(l+y^+/) = 2l{y+f). Divide troth members by y^;then we have

原文 This is as far as we can reduce this equation, without the aid of the other

equation; therefore clear the second equation of fractions, and we haveB0176｜原版スキャンp.16／原版本文p.9｜原…

原文 Equation [a] shosvs us that Q^^^J = 24^/3+5-30. Suhstituting this value of

G^/^nj in [b], we haveB0220｜原版スキャンp.19／原版本文p.12｜原文順0220｜ロビンソン本文原版記号・OCR転写を要照合：数式、単位、数表、天文値は巻末の原版…

原文 --JThrough the three points A, B and H, describe a circle; the line FH will touch

that circle at the point H. Join AH, BH, and the angle AHB is the angle required; andit is tbe gr…

原文 4. If, ffovn any two points in the circumference of a circle, there be dravm two

straight lines to a -point in a tangent to that circle, they will make the greatestangle when dra…

原文 S. if, from the tJvree angles of any triangle, lines be drawn to the points of

bisection of the opposite sides, these lines intersect each other in the same point.B0301｜原版スキャンp…

原文 The angle ABQ is a right angle, and equal to PBV. From each of these equals,

take away the common angkB0326｜原版スキャンp.29／原版本文p.22｜原文順0326｜ロビンソン本文『数学大辞典』p.102。

原文 Let ABC be the equilateral tjiangle in the circle ABC, and designate each side by

t. Take D any point in the arc BC, and join AD, BD and BC.B0351｜原版スキャンp.31／原版本文p.24｜原文順0351｜ロビンソ…

原文 Scholium. By factoring this eqiiatioii, we have {y+ztn-z) = (i+.)(6-a), or (y+z):

(b+a) - (6-.): (y-z) __.[p]B0393｜原版スキャンp.33／原版本文p.26｜原文順0393｜ロビンソン本文この比率は三角法に用いられることもあり、次のような一般的…

原文 Let AB be the given side, A the gif en angle, and AD the given difference of [he

other tivo sides.B0414｜原版スキャンp.35／原版本文p.28｜原文順0414｜ロビンソン本文DBに接続し、HでBDを二分する。

原文 But ' this manner of presenting scientific truth is not only unsatisfactory, but

perplexing. We must therefore elucidate.B0438｜原版スキャンp.37／原版本文p.30｜原文順0438｜ロビンソン本文直角に交わる二つの線を描きます…

原文 x^—px = q, or (^x—p'jx = q. Construct the figure as here represented, and it is

obvious thatB0462｜原版スキャンp.39／原版本文p.32｜原文順0462｜ロビンソン本文原版記号・OCR転写を要照合：数式、単位、数表、天文値は巻末の原版ページ画像を確認してく…

原文 The most diificult form of a quadratic is the following; x^—px = —q. In

respect to the signs, it is proper to remark, that in numbers and magnitudes, thereis no such thi…

原文 To iind the other root, take the logarithm of q already found, md from it

subtract hgx last found, thus: 6,256273 2,698969 log.... 3,556304.. N. —3600 bychanging signs. B0…

数式・計算（OCR転写）：y^~{4ap—4f)y^-~8bpy+{a^-i-'l^~

r^)4f = [G]原文 y^~{4ap—4f)y^-~8bpy+{a^-i-'l^~r^)4f = [G] B0604｜原版スキャンp.46／原版本文p.39｜原文順0604｜ロビンソン本…

原文 An equation with large coefficients is inconvenient for projection, as the

required circle would be correspondingly large; but we can readily transform anyequation into ano…

原文 44 MATHEMATICAl. KECKKAXIOUS. B0671｜原版スキャンp.51／原版本文p.44｜原文順0671｜ロビンソン本文ボラはMにあり、VPから2.8ユニット離れて…

原文 To show that we can determine the cuhe roof of any number (at least

approximately) by projection, we require the cube root of 4096; that is, find a rootof the equati…

数式・計算（OCR転写）：73 54原文 73 54 B0752｜原版スキャンp.54／原版本文p.47｜原文順0752｜ロビンソン本文原版記号・OCR転写を要照合：数式、単位、数表、天文値は巻…

158

property of the parabola, we find the angle nop = 109° 39' 45"; to which add Cop(34° 6' 30"), and…

原文 expression shows that the first member of equation [3] is a complete square,

on condition that we makeB0839｜原版スキャンp.58／原版本文p.51｜原文順0839｜ロビンソン本文原版記号・OCR転写を要照合：数式、単位、数表、天文値は巻末の…

原文 an equation showing that a and r are incommensurable with each other in this

case.B0867｜原版スキャンp.60／原版本文p.53｜原文順0867｜ロビンソン本文与えられた円の中で互いに触れ合うときcは与えられている。

原文 When any angle of a triangle:d, the base is cut proportionally to the sides of

the triangle. Put AB = X. Consider AE as the base of the triangle ABE; and as BDbisects the angle…

原文 Because the triangle BDC is rightangled at D, (he square on BD is equal to

BC.Bm, that is, equal to the rectangle Bn; but the square on BD is equal to cos^ \k,that is, B094…

原文 The angle BCD, being the exterior angle of the triangle ACB, is equal to the sum

of the angles at the base; and as DEB is at the circumference, and stands on thesame arc, DEB is …

原文 On the longer side as radius, describe a circle. Divide the diameter into two

parts AE, EG, so that AE shall he the sum of the sides; then EG will be thedifference of the side…

原文 gitude. Let SE represent the distance between the earth and sun at this

particular time; and to correspond with ourB1031｜原版スキャンp.71／原版本文p.64｜原文順1031｜ロビンソン本文例えば、地球の位置Eはa図…

原文 But AH is the sine of the arc PA, and CE is the sine of the arc PC. Let X = the

arc from P to the midway point between A and C, and put a = half the arc AC; then

B1101｜原版スキャンp.74／原版本文p.67｜原文順1101｜ロビンソン本文

(a;-6sinA)'a;-6sinA'。原文 (a;— 6sinA)' a;— 6sinA ' B1102｜原版スキャンp.74／原版本文p.67｜原文順1102｜ロビンソン本文原版記号・O…

原文 4. Given the latitude, the sun's dedinaiion, or the declination of any planet or

star, to find the semidiurnal arc for the svn, planet or star.B1135｜原版スキャンp.77／原版本文p.70｜原文順1135｜…

15, we obtain time; when we multiply time by 15, we obtain arc; hence 1 hour

multiplied by 15, gives 15°. Therefore the sum of the arcsB1154｜原版スキャンp.78／原版本文p.71｜原文順1154｜ロビンソン…

数式・計算（OCR転写）：1. N 14=00' W, Distance 15,20

chains = a;原文 1. N 14=00' W, Distance 15,20 chains = a; B1198｜原版スキャンp.81／原版本文p.74｜原文順1198｜Gummere…

38,72, and we have AH the distance required = 4,646, which ditfers from the given

answer about one livJc of the chain.B1228｜原版スキャンp.83／原版本文p.76｜原文順1228｜Gummere由来の問題・ロビンソンによる解説どんな…

原文 The area of the triangle GAB = 270,5 square chains; GA = 24,05, GB = 36,40:

hence GD = 73,69, GC=66,90. Let PQ be drawn parallel to DC, and let it divide thefield into tvi'O…

原文 The distance from O to the middle point of QD is one half of 41,19, or 20,59;

but this is greater by 3,89 than the distance from Q to the perpendicular from 0;that is, from Q …

原文 If the plane ACBD revolve on its axis CD, it will generate two equal cones; and

if from these we take the cylinder QR and the two small coaes on its ends, we shallhave the solid…

原文 Solving equation [1], we find three roots; one near 56, another 33,19 nearly,

and a third near the locality of mi««s 21, As neither the first nor the third canapply to our pro…

DIAG-P036｜原版スキャンp.36／本文p.29｜Geometrical Problems

DIAG-P038｜原版スキャンp.38／本文p.31｜Construction of Quadratic EquationsDIAG-P039｜原版スキャンp.39／本文p.32｜Constr…