1760 Arr. Samuel Foſter lis6. Having to numbers, 10 find a mean proportional. f

His is performed by the joynt uſe of Superficies and Lines: Let

the Numbers given be 20 and 45. Firſt, Icount the firſt number20 upon the Line of Superficies, then I take the ſame number 20 ouof the Line of Lines, with this length J open the Sector from thePoint 20 in the Line of Superficies, to ſome one Line on the other Leg,which iſſueth from the Center; afterwards J count 45 the other gi-ven number upon the ſame Line of Superficies; and from thencetake over the leaſt diſtance to the former Line on the other Leg, thismeaſured upon the Line of Lines, gives 30 for a mean proportionalbetween 20 and 45. i 8 g i

7. Having three Numbers given, nhereof the tmo firſt are ſuppaſed to beina duplicated proportion, hom to find 4 fourth, unto which the thirdſall e in the ſimple proportion of the former; that is, As the ſquare700fef the frſt to the ſquare root of the ſccond.

8 His ĩs lixewiſe to be performed by the joynt help of the Lines ofSuperficies and equal parts. Let the Numbers be, as 25 to 16, ſo40 to what? The two firſt terms are to be counted upon the Line ofSuperficies, becauſe between them the duplicated proportion is contai-

ned; and the other two muſt be taken upon the Line of Lines, becauſe

between them is the ſimple proportion contained. And to know uponwhat Line to work, IL order the terms ſo, as the firſt and third may beof one kind, thus, as 25 to 40, ſo 16 to what? Now becauſe 25 uponthe Line of Superficies(if to upon that Line be taken for 20 a wedo here take it) is greater than 40 upon the Line of Lines, therefor ethe lateral work muſt be done upon the Line of Superficier. So thatIts ke 40 oat of the Line of Lines, and put over that length from 25in the Line of Superficies unto the Line of Lines upon the other Legof the Sector. And the Sector being ſo opened, I count the thirdNumber 16 upon the Line of Superficies, and take over from thenceto the ſame Line of Lines. This length I meaſure upon the Line ofLines(from whence the ſecond Term was taken) and it reacheth to 3 2.So chat as 25 to 16, ſuppoſed to be in a duplicated proportion one tothe other, ſo is 40 to 32 in the ſimple proportion, whereof that otheris duplicated-—

8. Having