IQO philosophical transactions. [anno 1675. 



In the 8th triangle GHI, to find GI, IH. Toises Feet 



rOHI = 55° 58' O'/ The side GH 9695 O 



Angles <GIH= 27 14 O Hence G I 17597 O 



(lGH=96 48 O And HI* 21037 o 



Thus the 2d part of the three, viz. GI, is found. 



In the 9th triangle HIK, to find IK. 



CHIK = 65° 4& O" The side HI* 21043 O 



Angles -JhKI = 80 59 40 Hence IK* 11678 O 



CKHI = 33 14 20 



In the 10th triangle IKL, to find KL, IL. 



fLIK = 58° 31' 50" The side IK* ll683 O 



Ang es <^jj^-^ __ 5Q 3 J Q jj^^^^ j^L 1] 188 -2 



And IL 11186 4 

 In the nth triangle KLM, to find LM. 

 . , TLKM = 28° 52' 30'/ The side KL 11188 2 



^^^^\KML = 63 31 O Hence LM 6036 2 



In the 12th triangle LMN, to find LN. 

 ^^ ^^g fLMN = 60° 38' 0'' The side LM 6036 2 



"^^^\MNL = 29 28 20 Hence LN 10691 O 



In the 13th triangle ILN, to find NI. 

 The sum of the angles ILK, KLM, MLN, 



taken from 36o, there remains The sides LN 10691 O 



Angle ILN = 119° 32' 40'' And IL 11186 4 



Hence IN I8905 O 

 Thus, the line of distance, EN being as before said, divided into three un- 

 equal parts, EG, GI, IN, the measures of all three are found by this series of 

 triangles; viz. EG = 31897, GI = 17557, IN = I8905. These added 

 together, make the length of EN, which is the line of distance between Mal- 

 voisin and Sourdon, viz. 68359 toises. 



Now to continue this measure from Sourdon to Amiens, in order to verify 

 Fernelius's account; in fig. 8, R is the steeple of St. Peter's, in Montdidier; T, 

 a tree on the hill of Mareuil ; V, the lantern of Notre Dame, of Amiens. 

 To find the distance NV, observe NLM, the last triangle of fig. 7, and see how 

 it is disposed in fig. 9 ; where, in the triangle LMR, 



fLMR = 58'' 21' 50'-^ The side LM 6037 O 



^^ 1mRL = 68 52 30 Hence LR 5510 3 



In the triangle NRL ; 

 rNRL=115'' 1' 30" ThesideLR 5510 3 



^"^ \RNL = 27 50 30 Hence NR 7122 2 



* These two lines, HI and IK, are corrected from another calculation of them, in Picard's book. 



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