Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . arte 8fi wcJ. ^./Pa^f^4 . nn 00 U Sect. X. Mechanical Problems. 465 and d, by ad1 ; therefore the ftrength of all the between b and ay (the point D being ) will be dbz — da\ add the ftrength between€ and d, which is cdl \ and the ftrength of bitand cd, that is, the ftrength of the hollow beamis dbz—dal + cd\ But at the fection r the ftrengthis/;;1. W
Cyclomathesis : or, An easy introduction to the several branches of the mathematics; being principally designed for the instruction of young students, before they enter upon the more abtruse and difficult parts thereof . arte 8fi wcJ. ^./Pa^f^4 . nn 00 U Sect. X. Mechanical Problems. 465 and d, by ad1 ; therefore the ftrength of all the between b and ay (the point D being ) will be dbz — da\ add the ftrength between€ and d, which is cdl \ and the ftrength of bitand cd, that is, the ftrength of the hollow beamis dbz—dal + cd\ But at the fection r the ftrengthis/;;1. Whence if nr = ac> the ftrength at b to theftrength at r is as iix—Haz + cdl to db-^ca\l ; thatis, as db*— idcxca*—car to dbz—2dbxca+ca\Therefore if db- be the ftrength of the wholebeam, 2dc -f ca X ca will be the defect offtrength of the hollow beam, when it breaks at b \and idb—ca X ca, the defect of ftrength when itbreaks at n or f, which is greater than the former,And for the fame reafan the defect of ftrength tobreak at d, will be zba 4- ac x ca. PROB, CLXXXlV. $0 fupport a long prifmalic body horizontally by two A, B •, that it /hall asfoon break in A or Bas in C. Let DA = AF=:GB±:BE:=y, CF
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