第一部·星位数字的读法　第十四至十六则　对数与推运弧的均化

CANON XIV.

第十四则。

The use of the Sexagenary table is to find the part proportional, and will be proved, by example, in another volume of this work, to which we refer the Reader.

六十进制表的用处是求比例部分，将在本书的另一卷中用例子证明，请读者参阅。

CANON XV.

第十五则。

The Use of the Logarithms.

对数的用法。

We have placed the logarithms of absolute numbers, because in that manner of Ptolemean direction, which we follow, they are of very great service in exhibiting the fourth proportional number; therefore the three numbers being given, whether of parts or hours; if they are minutes, let each of them be reduced to minutes, adding them as they are disposed in their places; then take the logarithms of the third and second number, add them together; from this sum substract the logarithm of the first, and look for the remainder in the middle of the table; opposite to which, take the number for the fourth required, which divide by 60, and with the remainder you will have parts or hours with their minutes.

我们列出了绝对数的对数，因为在我们所遵循的托勒密式推运方法中，它们在求第四比例数上用处极大；所以，给定三个数，无论是度还是时；若带有分，就把每个数都化为分，按它们各自所处的位置加起来；然后取第三个数与第二个数的对数，相加；从这和数中减去第一个数的对数，在表的中间找这余数；与之相对，取所求第四个数的数，除以六十，商与余数就得到度或时及其分。

For example; let the numbers be given, the first 95, 25, the second 45, the third 100, 15, reduced to minutes are 5725—2145—6615; the logarithms of the first 375÷778, of the second 333.143, of the third 382÷053. I add the second and third together, and I make the sum 715196, from which I substract the first, and there remains the logarithm 339418, answering to the number 2478, which, reduced to degrees, makes 41° 18', the fourth number required.

例如：设给定三个数，第一个九十五、二十五，第二个四十五，第三个一百、十五，化为分是五千七百二十五、二千一百四十五、六千六百一十五；第一个的对数是三七五七七八，第二个的是三三三一四三，第三个的是三八二〇五三。我把第二个与第三个相加，得和数七一五一九六，从中减去第一个，剩下对数三三九四一八，对应的数是二千四百七十八，化为度，得四十一度十八分，就是所求的第四个数。

But because the logarithm of eight figures, the six first of these are sufficient for this purpose, and it seemed not good to rescind the rest, by reason of other advantages resulting from them: you may only make use of the six first, with provision, if you think proper, for it is of little use or consequence; but if the seventh figure be five or greater, you should add the unity to the six figures, which will be your last; and if the seven figures be 4, 3, 2, 1, 0, omit it entirely.

但因为对数有八位数字，前六位对此已经足够，而把其余的删去似乎不好，因为它们另有别的用处：你若认为合适，可以只用前六位，留有余地，因为〔后两位〕用处不大、关系不大；但若第七位是五或更大，就应在六位数上加一，作为你的末位；若第七位是四、三、二、一、〇，就完全略去。

In the given example of the first number 5725, the logarithm is eight figures, 37577755, I leave out the the two last figures 55, and add the unit to the six, which make it 375778. Observe also, that the logarithms are easier collected by taking two figures for every change; thus first collect 37, then 57, lastly 78.

在所给的例子中，第一个数五千七百二十五的对数是八位数三七五七七七五五，我略去最后两位五五，在第六位上加一，就成为三七五七七八。还要注意，每次取两位数，对数更容易收集；如先取三七，再取五七，最后七八。

CANON XVI.

第十六则。

To equalize the Arc of Direction.

均化推运弧。

Add the arc of direction to the right ascension of the natural Sun, look for this sum in the middle of the table of right ascensions under the ecliptic, and take the degree and minute of longitude corresponding with that sum; then in the best Ephemeris reckon in how many days the Sun from the day and hour of birth, has arrived at that degree and minute. The number of days indicate as many years; every two hours over reckon a month; for in the nativities which follow, the example is explained.

把推运弧加到本命太阳的赤经上，在黄道的赤经表中间找这个和数，取与之对应的黄经度与分；再在最好的星历中数一数，太阳从出生的日子与时刻起，要多少天才到达那个度与分。天数表示同样多的年；多出来的每两小时算一个月；后面所列的本命中有例子说明。