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viding the Degree: (Not that I intended to make a Difference, (or rather a Confufion, by intermixing them) but because these feveral Tradates were not written at the fame time, nor, at firft, intended to be joined together, as here they are: But fince it fo is, I have here (in the beginning) inferted a thort Table, by which Sexagenary Minutes are Reduced to Centefimal or Millefimal Parts: And alfo, Centefimal Parts to Minutes and Seconds: So that when the Reader meets with either of them, in any Part of thefe Tractates, he need not be at any Stand) (or Demurr about it) but readily know, to which Account it belongs, for the Manner of writing them will difcover it: So 23 Deg. 30 Min. is written as here; but the fame written Centefimally, thus, 23.5 Deg. Alfo 56 Deg. 43 Min. is written Sexagenarily, as here, but the fame Centefimally, thus, 56.71 Deg. or Millefimally, thus, 56.716 Deg. And fo of all others, as in the Table.


Of the Solution, Calculation, or Mensuration, of Rightangled Plain Triangles.


N Right-angled Plain Triangles, I call thofe Sides, which Fig. XII. comprehend the Right Angle, the Legs; and the Side fubtending the Right Angle, I call the Hypotenuse; and the Triangle which I fhall make ufe of in the Refolving the Seven CASES following fhall be that Diagram noted with M, in Fig. XII. Whofe Diagram Sides and Angles are,


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A B 235.00
BC 274 93
CA 142.72

Parts and Centefms.

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CASE I. The Legs A B and A C given, to find the Angle C. Fig. XII.


As Log. A C: Radius: Log. A B: C. [By Axi. I.

G 2


Cafe L

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Fig. XII. CASE II. The Angles C and B, and the Leg. A B given; To Cafe II. find the Leg. A C.


As Rad. Leg. A B::t B: Log. A C. [By Axi. I.

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Fig. XII. CASE III. The Hypotenufe BC, and the Leg. A B given, To

Cafe III.

find the Angle C.


As Leg. B C Rad.:: Leg. A B. s C. [By Axi. II.

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Fig. XII. CASE IV. The Hypotenufe BC, and the Angles B and C, gi

Cafe IV.

ven; To find the Leg. A B.


As Radius Hyp. B C:s C, Leg. A B. [By Axi. II.


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CASE V. The Angles B and C, and the Leg. A C, given; Fig. XII.

To find the Hypotenuse B C.


Ass B: Leg. A C:: Radius: Hypotenufe BC. [By Axi. II.


As Sine B, 31.27 Deg.

Is to Leg. A C, 142.72 Parts

So Radius, Sine 90 Deg.

9.7152273 12.1544848


Cafe V.

To the Hypotenuse B C, 274.93 Parts


CASE VI. The Hypotenufe B C, and the Leg. A C, given; Fig. XII. To find the other Leg. A B.


1.) As Leg. BC: Rad.:: Leg. A C:s B. [By Cafe I. 2.) As B: Leg. A C:: Rad.: Leg. A B. [By Cafe L

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Cafe VI.

Fig. XII. CASE VII. The two Legs, B A and C A, given; To find t Cafe VII. Hypotenuse B C.


1.) As Leg. A B: Rad.:: Leg. A C:t B. [By Cafe I.

2.) Ass B: Leg. A C:: Rad.: Leg. B C. [By Cafe V.

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The End of the Seven Cafes of Right-angled Plain Triangles.


Of the Solution (or Menfuration) of Oblique-angled
Plain Triangles.

Fig. XII. THE Triangle which I fhall make ufe of in the Solution Diagram the Five CASES of Oblique-angled Triangles, fhall S. that noted with S, whofe Sides and Angles are

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