M. Blundevile his exercises containing sixe treatises, the titles wherof are set down in the next printed page: which treatises are verie necessarie to be read and learned of all yoong gentlemen that haue not bene exercised in such disciplines, and yet are desirous to haue knowledge as well in cosmographie, astronomie, and geographie, as also in the arte of navigation ... To the furtherance of which arte of navigation, the said M. Blundevile speciallie wrote the said treatises and of meere good will doth dedicate the same to all the young gentlemen of this realme.

How to find out by the said tables, the distance betwixt two places differing both in Longitude and Latitude, making the totall Sine to be no more but 60/000.

THis is done by finding out two numbers, whereof the one is called in Latine Primum inuentum: that is to say, the first found number, and the other is called Secundum inuentum, that is the second found number in such order as followeth.

First then knowing the Longitude of either place, take the differēce of their Longitudes by subtracting the lesser Longitude out of the greater, that done, multiply the right Sine of that dif∣ference into the Sine of the complement of the lesser Latitude, and diuide the product of that Multiplycation by the totall Sine, and then séeke out the arch of that quotient according to the rule before taught, so shall you haue the first found number: That done, multiply the right Sine of the lesser Latitude by the totall Sine, and hauing diuided the product thereof by the right Sine of the complement of the first found number, subtract the arch of that quotient out of the greater Latitude, and you shall haue the second found number. Then multiply the right Sine of the complement of the first found number into the right Sine of the complement of the second found number, and hauing diuided the product of that Multiplycation by the totall Sine, séeke the Arke of that quotient in the tables, and take that Arke out of the whole Quadrant, and the degrées that doe remaine, are degrées of the great Circle, which if you multiply by 60. the product of y^t Multiplycation will shew you how many Italian miles the one place is distant from the other, or if you would haue Germane miles, thē multiply the fore∣said degrées of the great Circle by 15. or else diuide the product

of the Italian miles by 4. and you shall haue your desire. As for example, you would know what distance is betwixt Hierusalem and Noremberg a famous towne in Germanie, Hierusalem ac∣cording to Appian his tables, hath in Longitude 66. degrées 0′· and in Latitude 31. degrées, 40′· Againe Noremberg hath in Longitude 28. degrées, 20′· and in Latitude 49. degrées, 24′· the difference of their Longitudes is 37. degrées, 40′· the right Sine wherof is 36/664. for in this example Appian maketh 60/000. to be the total Sine, and therefore he reiecteth the two last fi∣gures en the right hand found in the first tables of Monte Regio. Now you must multiply 36/664. into the right Sine of the com∣plement of the lesser Latitude which Sine is 51/067. the product of which two Sines being multiplyed the one by the other, amoun∣teth to 1/872/320/488. which if you diuide by the totall Sine. 60/000. you shall find in the quotient 31/205. whose arch is 31. degrées, 20′· and this shall be your first found number. This done, multiply the right Sine of the lesser Latitude which is 31/498. by the totall Sine 60/000. and the product thereof wil be 1/889/ 880/000. which summe if you diuide by the Sine of the comple∣ment of the first found number which Sine is 51/249. you shall find in the quotient 36876. the Arke whereof is 37. degrées 55′· which arch being subtracted out of the greater Latitude, there will remaine 11. degrées, 29′· and that shall be your second found number, then multiply the foresaid Sine of the complement of the first found number which is 51/249. by the Sine of the comple∣ment of the second found number which is 58/798. and the pro∣duct thereof will amount to 3/013/338/702. which if you diuide by the totall Sine, you shall find in the quotient 50/222. the arch whereof is 56. degrées, 50′· which being subtracted out of the whole Quadrant which is 90. degrées, there will remaine 33. de∣grées, 10′· of the greater Circle, which 33. degrées, if you multi∣ply by 60. it will make 1980. miles, whereunto you must adde for the 10′· 10. miles, so shall you find the distance betwixt the two foresaid places to be 1990. Italian miles, which if you would re∣duce into Germaine miles, then diuide that number by 4. for 4. Italian miles doe make but one Germaine mile, so shall you haue 497. Germaine miles, and two Italian miles remaining, which is halfe a Germaine mile, which summe agréeth with that which

Appian setteth downe in his Geographie, whereas he vseth the selfe same example, and worketh it in like manner Per tabulas sinuum.