28087
omnia AZ x AE + BZ x BF + CZ x CG, &
c.
= {DHcub.
/3}
crunt omnia AZ x √ VAZ φ + BZ x √ VBZφ + CZ x
√ VCZφ, & c. = {DHcub/3} √{1/2} = √ {DH6/18. } Eſt autem DH_q_ =
2 VD ψ φ, vel DH6 = 8VD ψ φ {3/ }; quapropter omnia AZ x
√ VAZ φ + BZ x √ VBZφ + CZ x √ VCZφ, & c. = √
{8/18} VD ψ φ {3/ } = {2/3} √ VDψφ {3/ }.
crunt omnia AZ x √ VAZ φ + BZ x √ VBZφ + CZ x
√ VCZφ, & c. = {DHcub/3} √{1/2} = √ {DH6/18. } Eſt autem DH_q_ =
2 VD ψ φ, vel DH6 = 8VD ψ φ {3/ }; quapropter omnia AZ x
√ VAZ φ + BZ x √ VBZφ + CZ x √ VCZφ, & c. = √
{8/18} VD ψ φ {3/ } = {2/3} √ VDψφ {3/ }.
VI.
_Exempla._
Sit VDψ circuli quadrans (cujus radius dicatur
R, & Peripheria P) ſegmenta VAZ, VBZ, VCZ, & c. in ſi-
nus rectos AZ, BZ, CZ, & c. ducta conficient {R_q_P_q_/8. }
11Fig. 123.R, & Peripheria P) ſegmenta VAZ, VBZ, VCZ, & c. in ſi-
nus rectos AZ, BZ, CZ, & c. ducta conficient {R_q_P_q_/8. }
Item Summa AZ √ VAZ + BZ √ VBZ + CZ √ VCZ,
& c. = {2/3} √{R3P3/8. } = √ {R3P3/18. }
& c. = {2/3} √{R3P3/8. } = √ {R3P3/18. }
Si VD ψ ſit parabolæ ſegmentum, factum è ſegmentis in applicatas
erit {2/9} VD_q_ x Aψ_q_; ac è radicibus ſegmentorum in applicatas factum
erit {2/3} √ {8/2} { /7} VD3 x Dψ3 √ {3/2} {2/4} { /3} VD3 x Dψ3.
erit {2/9} VD_q_ x Aψ_q_; ac è radicibus ſegmentorum in applicatas factum
erit {2/3} √ {8/2} { /7} VD3 x Dψ3 √ {3/2} {2/4} { /3} VD3 x Dψ3.
Similia plura de factis è _Segmentorum poteſtatibus, autradicibus_
_aliis in applicatas, aut ſinus ductis_, hinc extundi poſſent.
_aliis in applicatas, aut ſinus ductis_, hinc extundi poſſent.
VII.
E dictis porrò ſequitur, ſi omnes ( vertici, &
perpendicula-
ribus interjectæ) VP per reſpectiva puncta A, B, C, & c. Concipian-
tur applicatæ, puta ut AY, BY, CY, & c. reſpectivis VP æquentur;
erit è ſic applicatis _conſtitutum ſpatium_ ADξθ _æquale ſemiſſe quadrati_
_ex ſubtenſa_ VH.
ribus interjectæ) VP per reſpectiva puncta A, B, C, & c. Concipian-
tur applicatæ, puta ut AY, BY, CY, & c. reſpectivis VP æquentur;
erit è ſic applicatis _conſtitutum ſpatium_ ADξθ _æquale ſemiſſe quadrati_
_ex ſubtenſa_ VH.
Nam, ob omnes VA + VB + VC, &
c.
= {VD_q_;
/2} &
omnes
AP + BP + CP& c. = {DH_q_,/2} liquet fore omnes VP =
{VH_q_. /2}
AP + BP + CP& c. = {DH_q_,/2} liquet fore omnes VP =
{VH_q_. /2}
VIII.
Porrò, ſi (poſitis iiſdem) ſit curva RXXS talis, ut ſit IX
= AP, & KX = BP; & LX = CP, & c. erit _ſolidum factum
= AP, & KX = BP; & LX = CP, & c. erit _ſolidum factum