第一部·星位数字的读法　第一则　由黄经与纬度求赤纬

How to UNDERSTAND the NUMBERS of the PLACES of the STARS.

怎样理解星辰位置的数字。

For greater distinction and perspicuity, I have divided the continuation of the rules into four parts.

为了更加分明清楚，我把规则的后续部分分为四部分。

The first contains the calculation of the places of the stars, in order to know their constitution under the primum mobile; for longitude and latitude with the situation of each of them in the world, and the distance from the cardinal signs and houses, the right and oblique ascension, the horary times, the semi-diurnal and nocturnal arcs, and many things of this kind.

第一部分包含星辰位置的计算，以便知道它们在第一原动天之下的构成；包括黄经与纬度，以及每颗星在世界上的位置，离四角与诸宫的距离，赤经与斜升，时辰的时间，半昼弧与半夜弧，以及许多这类的东西。

Secondly. Consists of methods, to compute the directions of the significator to the aspects in the Zodiac, and primum mobile.

第二，包含计算征象星向黄道上与第一原动天中的相位推运的方法。

Thirdly. The calculations of the directions, to the aspect received in the world.

第三，向世界上所受相位推运的计算。

Fourthly. The observations and precepts of the progressions, ingresses, transits, &c.

第四，关于进程、进入、行经等等的观察与规则。

But, because all the tables confine their numbers to the whole degree, both of latitude and longitude, as often as the given place is in the degree and minutes, either by length or breadth, the proportional part corresponding with those minutes, is to be taken with the given place, both beyond the degree; concerning which, in the first Canon or rule, where a method is explained for young beginners; and also, in the Canon of the use of the Sexagenary tables, that it might be sought in vain whenever it happens that the proportional part is to be taken; it is therefore to be observed, that the method is always the same as in the first and fourteenth Canon, consequently, it is ever, and on all occasions, to be looked to and preserved.

但因为一切表格的数字都只列到整度，无论纬度还是黄经，所以每当给定的位置带有度和分，无论在黄经还是纬度上，都要随给定的位置取与那些分相应的比例部分，两者都在整度之外；关于这一点，在第一则中为初学者讲解了一种方法；在六十进制表用法的那一则中也有，以免每逢要取比例部分时却无处可寻；因此要注意，这方法始终与第一则和第十四则中的相同，所以在任何场合都要遵照、保持。

CANON I.

第一则。

To take the Declination of the Planets from the Declination of the Longitude, in the Ecliptic.

由黄道上黄经的赤纬求行星的赤纬。

The table of declinations, contains six signs in the first part, and six in the last; those under the left columns have the degree of longitude descending, but those on the right, ascending: it is divided into two parts, viz. into north and south latitude, the degree of which latitudes are seen under their denominations. It is likewise divided by the intermediate scale, into north and south declination; that in the former place, i. e. above the scale, is placed below the scale of the southern.

赤纬表在前半部分列六个星座，后半部分列六个；左栏下的黄经度数是下行的，右栏的则是上行的：表分为两部分，即北纬与南纬，其纬度的度数见于各自的名目之下。表又被中间的分隔线分为北赤纬与南赤纬；北赤纬在前面，即在分隔线之上，南赤纬则在分隔线之下。

If the given place, whose declination you want to know has no latitude, seek for that under the column of latitude 0°, which is in the ecliptic; and if it be in the integral parts, in ♌, 24° 0', under the column of 0°, over against ♌, 24°, you will have the declination 13° 34': but if the given place be in the parts and minutes, suppose in 24° 10' of ♌, the proportional part belonging to the 10' must be taken from the difference, which is 24° between the declination, and 25° of ♌; the declination of 24° of ♌ is 13° 34'.

若给定的位置，即你想知道其赤纬的那个位置，没有纬度，就在纬度零度的栏下找，那就是黄道上的；若它在整度上，比如狮子二十四度零分，在零度栏下、对着狮子二十四度，你会得到赤纬十三度三十四分：但若给定的位置带有度和分，假定在狮子二十四度十分，就必须从二十四度的赤纬与狮子二十五度的赤纬之差中，取属于这十分的比例部分；狮子二十四度的赤纬是十三度三十四分。

But 25° gives 13° 14' declination: the difference between the two declinations is 20, wherefore, by the golden rule, I say, if the integral part, i. e. 60 gives 20, what will 10 give? Answer, 3', taken from the declination 13° 34', which is facing 24° of ♌; because the declination is less, (but if it should be increased it ought to be added) and there remains for the declination of 24° 10' of ♌, 13° 31'; but if the given place has a latitude, and is in the integral degrees both for longitude and latitude, at one view you will have its declination; viz. in the angle.

而二十五度得赤纬十三度十四分：两个赤纬之差是二十，因此，按黄金法则，我说：若整的部分即六十得二十，十得多少？答：三分，从对着狮子二十四度的赤纬十三度三十四分中减去；因为赤纬在减小（但若是增大，就应当加上）；于是狮子二十四度十分的赤纬剩下十三度三十一分；但若给定的位置有纬度，且黄经与纬度都在整度上，你一眼就能得到它的赤纬，即在两栏相交的格中。

Suppose then the given place 24° of ♌ with 2° north in the common angle, you will have the declination 15° 27'. But if it be according to longitude in degrees and minutes, and for latitude in the integral degree, the proportional part is to be taken from the difference of the declination of the greater and lesser degree of longitude, between which is the given minute, under the column of the said latitude.

那么假定给定的位置是狮子二十四度、北纬二度，在共同的格中，你会得到赤纬十五度二十七分。但若黄经带度和分，纬度在整度上，就要在该纬度的栏下，从给定的分所在的较大与较小两个黄经度数的赤纬之差中取比例部分。

Let the place be in 24° 10' of ♌, with 2° north, under the column north, with 2° for the longitude 24° 0', the declination is 15° 27'; and for the longitude 25° 0', under the same column, is found 17° 7'; the difference of those declinations is 20°, from which the 10° 3' is substracted, as before.

设位置在狮子二十四度十分，北纬二度，在北纬栏下、纬度二度，对黄经二十四度零分，赤纬是十五度二十七分；对黄经二十五度零分，在同一栏下，查得十七度七分；这两个赤纬之差是二十度，从中如前减去十度三分。

If the given place be through longitude in the integral degree, and latitude in the degrees and minutes, the proportional part must be taken from the difference of the declination of the greater and lesser degree of latitude, between which is the given minute, and to the same longitude; that if the given place be 24° of ♌, with the latitude northern 2° 51', under the latitue 2°, the declination is 15° 27'; under the latitude 3°, the declination is 16° 24', and the difference is 57'; from which, for the 51', will be found by the golden rule to give 48' to be added, because the declination is increased by latitude.

若给定的位置黄经在整度上，纬度带度和分，就要在同一黄经下，从给定的分所在的较大与较小两个纬度的赤纬之差中取比例部分：例如给定的位置是狮子二十四度，北纬二度五十一分，在纬度二度下，赤纬是十五度二十七分；在纬度三度下，赤纬是十六度二十四分，差是五十七分；按黄金法则，从中为五十一分求得四十八分，要加上，因为纬度使赤纬增大。

Lastly, if the given place be by longitude and latitude in degrees and minutes, as in the nativity of Sebastian, King of Portugal, the Moon's place, according to longitude, as in 24° 10' of ♌, with 2° 51' north, the proportional part must be taken doubly; wherefore, substracting the 3' from 15° 27', there remains 15° 24'; but by adding the 48', there remains the Moon's declination 16° 12'.

最后，若给定的位置黄经与纬度都带度和分，比如在葡萄牙国王塞巴斯蒂安的本命中，月亮的位置按黄经在狮子二十四度十分，北纬二度五十一分，就要取两次比例部分；因此，从十五度二十七分减去三分，剩十五度二十四分；再加上四十八分，得月亮的赤纬十六度十二分。

To take the proportional part, you have the logistical logarithms, or sexegenary table: its use is shewn in the fourteenth Canon, though the golden rule may likewise serve; but this method of calculating is to be rightly understood; for in all the tables it would be too tedious always to repeat it.

取比例部分，可用比例对数表，即六十进制表：其用法见第十四则，不过黄金法则也可以用；但这种计算方法须正确理解；因为在所有的表中每次都重复它，就太冗长了。

In the scale which divides the northern declination from the southern, care should be taken as often as it happens to pass through the scale, from one part to the other, either into longitude or latitude, to have the declination conjoined; and there will be a very great difference; from which, substracting the proportional part, if it be less than the declination of the former angle which belongs to the integral degrees, either the longitude or latitude is to be taken from the declination of that angle, and there will remain the declination of the same denomination; but if, on the contrary, the proportional part taken be greater, the former must be taken from the latter, and the remaining declination changes the denomination.

在分隔北赤纬与南赤纬的那条线上，每当无论黄经还是纬度的变化跨过这条线，从一边到另一边时，都要注意把赤纬合起来；这样差就会很大；从中减去比例部分，若比例部分小于整度所属的前一格的赤纬，就从那一格的赤纬中减去，剩下的赤纬名目不变；但若反过来，所取的比例部分较大，就从后者中减去前者，剩下的赤纬改换名目。

Let the Moon be in 9° 10' of ♎, with 4° north, I add the 6' to the 18', and the difference is 24'; from which, to the 10', 4' is due: these, as they are less than 6', I substract from the 6', and there remains the declination 2' north.

设月亮在天秤九度十分，北纬四度，我把六分加到十八分上，差是二十四分；从中为十分得四分：这四分小于六分，我就从六分中减去，剩下北赤纬二分。

Suppose the Moon in 9° 40' of ♎, from the difference for the 40', 16' is due; which, as they are more than 6', I take 6' from the 16', and there remains the Moon's declination 0° 10' south; but if the Moon in this case should have 4° 30' north, I add 18' to the 38', which are under 4 and 5, and the difference is 56'; from which, for the 30', 28' are due: from these, as they are more than 10', I substract the 10', and there remains the declination 0° 18' north.

假定月亮在天秤九度四十分，为四十分从差中得十六分；这比六分多，我就从十六分中减去六分，剩下月亮的赤纬南零度十分；但若月亮在这种情形下有北纬四度三十分，我把十八分加到四度与五度下的三十八分上，差是五十六分；从中为三十分得二十八分：这比十分多，我就从中减去十分，剩下赤纬北零度十八分。

Again, if they are fewer, suppose 5', I should take these 5' from 10', and the declination is 0° 5' south. The given declination is brought back to the degree in the ecliptic in this manner; however, if it be not greater than 23° 32'; for otherwise it would fall out of the ecliptic, under the column of latitude 0° 0', that is, of the declination of the ecliptic.

又，若它们较少，假定五分，我就从十分中减去这五分，赤纬是南零度五分。给定的赤纬要这样还原为黄道上的度数；不过它不得大于二十三度三十二分；否则就会落出黄道之外，即在纬度零度零分的栏下，也就是黄道赤纬的栏下。

Let the given declination be sought for, and above the scale of the northern; but below, if southern; but if it should be found even to its minutes, the degree of the signs in the ecliptic corresponding with it, are those which are placed opposite on both sides; but if the minutes of the given declination are not expressed, the proportional part is to be taken, instead of the minutes that are wanting to be added or substracted from the degree in the ecliptic, &c. in this manner:—Let the south declination be 7° 28' under the scale, and in the column of latitude 0°, I find it opposite to 19° of ♎, or in 11° of ♓, therefore it answers to these degrees.

给定的赤纬，若是北的，就在分隔线之上找；若是南的，就在线之下找；若能找到分毫不差的，与之对应的黄道星座度数，就是两边相对排列的那些；但若表中没有给定赤纬的分数，就要取比例部分，代替所缺的分数，加到黄道度数上或从中减去，等等，方法如下：设南赤纬七度二十八分，在分隔线之下、纬度零度的栏中，我发现它对着天秤十九度，或双鱼十一度，所以它对应这两个度数。

In the nativity of Sebastian, King of Portugal, the declination of ♄ is 7° 47', which is not expressed in the table; but I take the next less, 7° 28', then the next greater is 7° 51'; the difference of these is 23': the declination of ♄ exceeds the less by 19'. I then ask, if the whole difference of 23' give 60' of longitude, how many will 19' give?

在葡萄牙国王塞巴斯蒂安的本命中，土星的赤纬是七度四十七分，表中没有列出；于是我取下一个较小的，七度二十八分，再下一个较大的是七度五十一分；两者之差是二十三分：土星的赤纬比较小的多十九分。于是我问：若整个差二十三分得黄经六十分，十九分得多少？

Answer 50', which are to be added to the 19° of ♎; so that ♄'s declination corresponds with 19° 50' of ♎, or with 10° 10' of ♓: the same happens if the proportional part be taken differently; for the next greater declination exceeds ♄'s declination by 4', for which the proportional part is 10', which are added to the 80° of ♓, or the 20° of ♎, from the place of the ecliptic, as before.

答：五十分，要加到天秤十九度上；所以土星的赤纬对应天秤十九度五十分，或双鱼十度十分：若换一种方式取比例部分，结果也一样；因为下一个较大的赤纬比土星的赤纬多四分，与之相应的比例部分是十分，把它们加到双鱼八十度上，或从天秤二十度上减去，如前一样从黄道的位置得出。