An Excellent TABLE for the finding the Periferies or Circumferences of all Elleipses or Ovals, so near the Truth as any Mechanical Practice can require,

Calculated with great Diligence and Care by Sir JONAS MOORE, and not done before.
Axis Perife­ries Diff. Axis Perife­ries Diff.
  2.0000   50 2.4218  
1 2.0012 12 51 2.4342 124
2 2.0028 16 52 2.4467 125
3 2.0048 20 53 2.4594 127
4 2.0072 26 54 2.4723 l29
5 2.0100 28 55 2.4852 129
6 2.0133 33 56 2.4983 131
7 2.0170 37 57 2.5114 131
8 2.0213 43 58 2.5245 131
9 2.0261 48 59 2.5377 133
10 2.0314 53 60 2.5510 133
11 2.0370 56 61 2.5644 134
12 2.0432 62 62 2.5779 135
13 2.0496 64 63 2.5915 136
14 2.0564 68 64 2.6052 137
15 2.0634 70 65 2.6189 137
16 2.0708 74 66 2.6327 138
17 2.0784 76 67 2.6465 138
18 2.0862 78 68 2.6604 139
19 2.0942 80 69 2.6744 140
20 2.1024 82 70 2.6884 140
21 2.1106 82 71 2.7025 141
22 2.1192 86 72 2.7166 141
23 2.1281 89 73 2.7309 143
24 2.1373 92 74 2.7453 144
25 2.1467 94 75 2.7599 146
26 2.1561 94 76 2.7745 146
27 2.1658 97 77 2.7891 146
28 2.1756 98 78 2.8038 147
29 2.1856 100 79 2.8186 148
30 2.1956 100 80 2.8334 148
31 2.2057 l01 81 2.8482 148
32 2.2160 103 82 2.8630 148
33 2.2264 104 83 2.8779 149
34 2.2368 104 84 2.8929 150
35 2.2474 106 85 2.9080 150
36 2.258l 107 86 2.9231 151
37 2.2692 111 87 2.9382 151
38 2.2803 111 88 2.9534 152
39 2.2915 112 89 2.9686 152
40 2.3028 113 90 2.9839 153
41 2.3142 114 91 2.9993 154
42 2.3256 114 92 3.0147 154
43 2.3371 115 93 3.0302 155
44 2.3488 117 94 3.0458 156
45 2.3607 119 95 3.0614 156
46 2.3726 119 96 3.0771 157
47 2.3848 122 97 3.0928 157
48 2.3970 122 98 3.1086 158
49 2.4094 124 99 3.1244 158
50 2.4218 124 ⊙ 3.1402 158

EXAMPLE I.

WHere the longer Axis of the Elleipsis is 1, and the shorter .78; Because the Table is made for such Elleips's, enter with .78, the Perifery of that Elleipsis will be 2.8038.

EXAMPLE II.

The longer Axis 1, the shorter .4382, I enter with .43, gives 2.3371: Then to find the part answering to .71, say, If 100 give .117; what shall .71 give? Answ. .83, which added to 2.3371, gives 2.3454 for the Perifery desired.

EXAMPLE III.

Where the longer Axis is 388, the shorter 280, first say, 388 : 280 :: 1.000 : Answ. .721, seek in the Table for .72, it gives 2.7166; then say, 1.0000:2.7166 :: 388 : Answ. 1054.06, which is the Circumference desired.

EXAMPLE IV.

The longer Diameter 32.54, the shorter 18.64; say; 32.54 : 18.64 :: 1.000 : 572; to which in the Table answers 2.5114, and the part proportional for 2 is 26, which makes the whole 2.5140; then 1.000 : 2.5140 :: 32.54 : 81.805 the Perifery required. The Area or Superficies of an Elleipsis is easily got by this Rule. As the longer Diameter, is to the shorter: So is the Circle of the longer Diameter, to the Elleipsis.

I have made above 45000 Arithmetical Operations for this Table, and am now well pleased it is finished. Some perhaps may find shorter ways, as I believed I had my self, 'till advised otherwise by the truly Honourable the Lord BRUNCKER. I therefore pursued the Rules given by me, in that Contemplation of the Elleipsis Printed in my Arithmetick, taking 100 Elleipsis betwixt that which falls upon the Diameter equal in this case to 2.0000 the first in the Table, and the greatest which is the Circle 3.1402 the last.

SOLI DEO GLORIA.

LONDON, Printed by W. G. for N. Brooke, at the Angel in Cornhill, 1676.

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