Full text: Clavius, Christoph: Geometria practica

GEOMETR. PRACT. nebitur altitudo A E, vel latus AD, in diſtantia ſecundum hunc numerum 500. quòd 1000. diuiſa per 2. dent Quotientem 500. At vmbra verſa trium mille-
ſimarum dabunt Quotientem 333 {1/3}. quià priori differt hoc numero, 166 {2/3}. Ex
quo intelligi licet, quando vmbra verſa abſciſſa valde parua eſt, magnum poſ-
ſe errorem committi in diſtantia inueſtiganda. Cum enim partes milleſimæ ſint
perexiguæ, facilè decipi poſſumus, vt nimirum putemus, ab ſciſſas eſſe tres mil-
leſimas, cum fortaſsis ſolum duæ abſciſſæ ſint: ac proinde err or committi po-
terit 166 {2/3}. altitudinem AE, vellaterum A D, qui error contemnendus non eſt. At quando partes vmbræ verſæ plures milleſimas continent, non tantus error
committitur, etiamſi vnam milleſimam pro altera accipiamus. Nam ſi verbi
gratia putemus, ab ſciſſas eſſe partes {30/1000}. ex vmbra verſa, cum verè abſciſſæ
ſint {31/1000}. error fieri poterit ſolum in 1. altitudine A E, vellatere A D, & {7/93}. cum {30/1000}. dent Quotientem 33 {1/3}. at {31/1000}. Quotientem offerant 32 {8/31}. Itaque magis probo, vt Quadratum in altiori loco ſtatuatur, quam in plano
Horizontis, quia ibi plures partes vmbræ verſę abſcinduntur, quam hic, vt con-
ſtat in diſtantiis æqualibus E F, D M. Vides ergo magnam eſſe adhibendam
diligentiam, vt accuratè partes milleſimæ rep eriantur per ea, quæ lib. 1. cap. 2. Num. 14. ſcripſimus.

Iam verò, ſi quadratum conſtructum ſit ad certam aliquam menſuram, hoc
eſt, vt latus contineat vel 1. paſſum, vel 1. cubitũ, vel 2. pedes, aut palmos, aut 3. aut 4. & c. res erit expeditiſsima, ſi ſemel tantum latus particularum 1000. du-
catur in menſuras, quibus latus æquiualet. Ita enim in longitudinibus ex-
quirendis, ſi quadratum ſupra planum, in quo eſt longitudo, ſtatuatur, (vt fit
in omnibus hypotenuſis, ſiue diſtantiis à loco menſoris vſque ad aliquod pun-
ctum menſore ſublimus, depreſsiuſue, quemadmo dum patuitin proxima figu-
ra, quando longitudo D M, inquiſita eſt, patebitque in ſcholio problematis 7. & in ſcholio problem. 9. Item in problem. 15. Num. 5. & in problem. 26. Num. 3. & in problem. 27. Num. 3. nec non in problem. 37. & 38. Num. 3. & denique in problem. 43. & 44. & in aliis locis) diuidendus ſolum eſt numerus
productus per partes vmbræ verſæ (quæ ſemper abſcinditur) notatas. Quo-
tiens enim dabit longitudinem quæſitám in data menſura. Verbigratia, ſi in vno
latere comprehendantur 3. pedes, multiplicabimus latus 1000. per 3. efficie-
muſque 3000. Ita que ſi in inueſtiganda longitudine quapiam abſciſſæ ſint par-
tes 200. ex vmbra verſa, partiemur 3000. per 200. Nam Quotiens 15. dabit 15. pedes pro quæſita longitudine. Nam cum in proxima figura ſit, vt vmbra verſa NB, 200. ad latus BA, 1000. Italatus AD, 3. pedum ad DM, multiplican-
dum eſt latus 1000. per 3. pedes, & productus numerus 3000. per 200. diuiden-
dus. Eademque decæteris ratio eſt. Sic ſi latus contineret {1/2} cubiti, diuidendu@
eſſet numerus 500. ex {1/2}. in 1000. procreatus per vmbram verſam. Pari ratio-
ne ſi latus complecteretur 10. palmos, diuidendus eſſet numerus 1000. genitu@
ex 10. in 1000. per vmbram verſam: vt in Quotiente prodeant palmi in longi-
@udine contenti, & c. quod non indiligenter notandum eſt.

106.1.

4. ſexti.

107. ALITER

5. Qvando diſtantia metienda magna eſt, & adeſt bona planities campi,
vti poterimus Quadrato ſtabili commodiſsimè hoc modo. Sit diſtantia obla-

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