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portional to S,A and S,B, ♪ (S,A—B)= S,A. S,B.

αβ

αβ

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(S',A-S',B) = (Proposition III. cor. 5. Trigonometry,)

αβ

% (S,A +B.S,A—B), or d=8.S,A+B. But the sine of

the sum of A and B is the same as that of their supplement C, or of the angle contained by the sides a and 8; and consequently dis

αβ

2

the third part of .S,C, the area of the triangle, or the third part of the excess of the angles of the spherical, above those of the plane, triangle. Wherefore the sines of the sides, which, in the spherical triangle, are as the sines of their opposite angles, are likewise proportioned, in the plane triangle, to the sines of those angles, increased each by the common excess. It is hence evident, that the angles of the plane triangle are obtained from those of the spherical, by deducting from each the third part of the excess above two right angles, as indicated by the area of the triangle.

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part of a second. Hence each angle of the small spherical

I

75.88

[blocks in formation]

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Page 32, line 2 from the bottom, for CED read EDC.
43, line 4, for BH read BE.

47, line 4, for E, read EC.

53, line 3, from the bottom, for CD read AD.

55, lines 12, 13, & 14, for DF and CD read CD and DF.

66

57, line 7 from the bottom, for "rectangles are” read “ rectangle is."
58, line 6, for CAD read AČF.

62, line 3, for ED read DB.

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line 17, for EI, CL, AC and BC, read FD, HM, GP and NB.

65, line 3, for DH read BH.

66, line 21, for AC read FB.

69, line 7, for BE read BC.

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lines 18 and 19, for AE and CE read AC and DE.

73, line 4 from the bottom, read "twice the square of BF and of."
79, line 11, for DE read DB.

84, line 12, read "two equal straight lines,"

108, line 24, for AC and CB read AB and AD.

109, line 9 from the bottom, for AFD read ADF.

129, line 9 from the bottom, for " isosceles" read "equilateral."

132, line 8 from the bottom, for DE read DA.

133, line 23, for BD read DE.

141, line 17, for FAD read FAE.

162, line 4 from the bottom, for D read C.

168, line 9, read "m:p::q:n."

170, lines 10, 11, and 12, read "B contain C" and "C contain D."

178, line 3 from the bottom, for "conversion" read "composition."
198, last line, read A: C:: C: B.

203, line 10, for DG read DA.

246, line 17, for BED read BEF.

lines 18 and 19, for DBC read FBC.

line 20, for ABD and BDA, read BAF and AFB.

line 21, for ABD read ABF.

line 23, for BD read BF.

248, line 18, for H read K.

249, at the top, for MH read MK.

line 19, for HB read HG.

251, line 12, for MOLH read MOKH.

252, lines 12 and 13, for CG and GB, read BG and CG.

297, line 3 from the bottom, for CB and CD read CD and CB.

300, line 9, for G read O.

304, line 6, for PGE read GFE.

310, lines 4 and 6 from the bottom, for CB and CD read CD and CB.

321, line 6 from the bottom, for D read F.

322, line 4, for EC read ED.

line 6, for C read D.

$28, line 16, for AC: AB, read AB: AC.

335, line 23, for " and AG," read "XAD."

349, line 9, for CB read AB.

359, lines 9 and 10, for IM and IH, read IH and IN.

360, lines 2, 3, 5, and 8, for CD and GH, read BD and FH

369. line 6 from the bottom, for G read D.

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