531 / 798
Liber
Demonthatio. (
Per
11.pr!mi huj1u
)
li~ea
BG
etl: apparencia linea: zqua.lis ipli AB, AF, nem eíl:
apparcntia linea: zquahs e1dcm AB; AC, BC,
func apparemiz linearum ad tabellam .rc6larnm ;
ideoque anguli A
lle
B, Cune apparem1:i: angulo-
,.!
!~º'"'"
'
"=
!;""
FG
5
~
3
conjungcmis \» ral\ebs
' apparenna me:c
tia linea: para\leb:,
&
"'~~a~;~1~c~;íl:
apparcn-
Porcrar una tantum
dil
1P
·
punél:um G, duci
paral\cl~t~'.~e~ ~~.duci,
&
per
~@~~~OO~~~~~~®®OO~!l!ll1!1~~11.!2l1!1~~®00~~~@00®00®@@@~~002fill2~~~
P R O
P O
S
I T
1 O
l l.
Problema.
!2!!11dratmn e:.: 11ng11lo viftm•
dcfcriberc.
~adrati deícribend~ diagon~lis
transfrrn–
íur in lineam terr:i: , h1nc mde m A B , A C.
Ex punél:o A ducanrur
linea: diagonales. ad
punél:a ditl:antia: E
&
F , finque A E , AF; 1rem
ex B ducarnr ad punll:um diíl:antiz. oppoli–
rum linea BF,
&
ex C linea C E; d1co li'gu·
tam AGHI,
e(fe
apparemiam quadrati cujus dia–
gonalis AC.
pemontl:rario. Linea: AE, CE, íunt repra:íen–
tationcs hnearum horizonralium,
&
paralielaruni .
(
pcr
1
¡.
1.
h1<j11J)
idem dico de B F, A F; igirur
quadrilaterum AGHI,eíl: repra:Íenratio parallelo–
grammi, anguli·amem in A, G, H,
1, (
p<r
1
¡.
1.
hrtj1u)
íum reél:i; igirur figura AGHr,etl: rell:an•
gula.Sum irem latera GH,
l-11
a:qualia,(per
e.w–
dem)
itcm Al,& AG.
~~~00~~®~~!1!1l'll!®~~~!l!ll1!1~~®®~00®~~~00~~®~@00~~~~~~~~@~
PROPOSITIO
111.
Problem·a.
01tadratmn diretle viji1m delineare
,
&
dividere,
&
fi•bdividere in alia quadrata
-<-
infaripta vifa
e,-.
angulo:
E _________ __ _ _D
F
B
../1
Ha:c figura ex aliis componituL Sir quadra–
tum cujus larus BC, primo defcribendum,
fe–
cundo dividcndum. Larus BC, dividatut bifariam
in A, mm ex B, A, C ducanmr linea: ad punéVJin
principalc D;
&
ex punllis B
&
C ducanmr ad
punél:a ditbmi:i: F
&
E, linea: BF,CE:fecaotes ra–
dios BD•, CD in punllis l
&
K ducaturque reél:a
1
K : rum ex puni!lo A d.;cantur reél:a: linea: ad
eadem punél:a ditl:antia: E
&
F, qua: fecabum ra–
dios B O , C O in G
&
H ex quibus duél:a: linem
~d
pun6\:a A
&
O quadratum exangulo vifum
-cxhi\nbunr.
Drmonílratio. Clarnm cíl: figurnm
BK,
elfe
ap–
parenriarn quadrati pcr primam hujus, irem
(per13.
1.hujus)
BK, CI effediagonales ,
& (
pcr
2.hu·jus)
AGOH, effc quadrarnm viíum ex angulo,
&
ita deinccps.
Si fecundum quadratum inrra primmn deícri–
bendum effet,eodem mod.o foret operandum circa
lineam KI, quo operati Íumus circa lineam BC.
Notandum item eíl: candem effe opcrarionem,
live punél:um principale
Ítt
ad latera, {ivc lir
~i
reél:e quadrato oppalirnrn ; non muranr_ur cnmr
praxes, neque eciam murancur demoníl:rac1ones.
®®~~~®~®~~®~~~~!1!l!N®~l1.!2l1!100~@~@~~@~~~~~~~~~~~~~~@~
P R O P O S 1 T 1 O
IV,
Problema.
,
Cirrnlum defcribere.
.
Ut circuli horizontaliicr pofüi , habeas app•·
frntiam ; circa illum quadmum defcribe
ABCJ;1~
·
-qova