Benedetti, Giovanni Battista de
,
Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]
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THEOREM. ARIT.
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83
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file
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0083
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0083
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te verò à ſecundo milliario vno primus antecedatur, ex communi ſcientia neceſſe
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eſt ſecundum tot diebus
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primo iter agere quot ſunt
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qui ſimul æquales erunt
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u.n.</
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ſed
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minor eft numero milliarium diurnorum primi vnitate
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>.e</
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. </
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<
s
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xml:space
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">Itaque rectè
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ſequemur regulam, quæ iubet ex numero milliarium vnitatem demere, quo nu
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merum dierum habere poſſimus.</
s
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</
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<
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<
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xml:space
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.</
head
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<
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<
s
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xml:space
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">SI verò ſecundi viatoris progreſſio per ternarium aſcenderet, ſumpto initio ab
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ipſo ternario, animaduertendum eſt an numerus milliarium diurnorum primi,
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ternario menſuretur necne, etenim ſi menſuretur, tandem aliquando paria millia-
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ria conficient, quæ dies ſit
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</
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<
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">quare ſub
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0083-01
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xlink:href
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</
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<
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>u.n.</
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totidem quot ſupra termini
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,
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&
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tertia ſit pars
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ex .95. theo-
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remate. </
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<
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xml:id
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xml:space
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">Itaque tota
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>.o.f.</
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minor erit
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duabus tertijs
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vnitate, vtiam re-
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ctè ſumendæ ſint duæ tertiæ partes
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>.u.n.</
var
>
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ex quibus vnitas detrahatur ſuperſitq́ue
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numerus
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dierum quæſitorum.</
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</
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xml:space
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num
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.</
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<
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<
s
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xml:space
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">CVM verò milliarium numerus p rimi viatoris metirinon poterit à numero
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aſcendente ſecundi, patet nullam futuram diem qua pari milliaria conficient,
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</
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>
<
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xml:space
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">quare illa vltima qua primus ſecundum antecedet, vno aut duobus milliaribus an-
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tecedet in præſenti caſu. </
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>
<
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xml:space
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">Antecedat itaque duobus milliaribus,
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dies
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>.u.n.</
var
>
& alte
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ra
<
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>.t.i.</
var
>
ſecundus primum vno milliari ſuperabit, ita quod ſub
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>.t.i.</
var
>
non poterunt plu-
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res integros dies iter agere, quam ambulauerunt ante diem
<
var
>.u.n.</
var
>
hoc eſt vſquequo
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ſecundtis iunctus ſit primo, qui numerus dierum, tertia parte
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var
>.o.n.</
var
>
ipſius
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>.u.n.</
var
>
vnitate
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minor erit, cum ex .95. theoremate
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>.o.n.</
var
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ſit tertia pars
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>.u.n.</
var
>
ex quo numerus
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>.o.f.</
var
>
ter-
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minorum aut dierum intergrorum cognitus erit, qui ſi cum numero alcendente
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cognoſcetur, ſtatim ex .99. theoremate deueniemus in cognitionem vltimi diei in
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tegri
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var
>
atque ita etiam totius ſummæ progreſſionis ex .95. theoremate. </
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<
s
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xml:space
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">Iam verò
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cognito numero milliarium diurnorum primi, ſimul cum numero terminorum, aut
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dierum conſequenter nouerimus rectanguli ſummam, hoc eſt productum à primo
<
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viatore formatum, quarum duarum ſummarum in præſenti caſu ſemper ea, quæ
<
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huiuſmodi producti eſt, maior erit, cum conſtitutum fuerit ſecundum viatorem à
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primo ſuperari ipſa die
<
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var
>
vno milliari amplius quam ſequente die
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>.t.i.</
var
>
primus à ſe
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cundo ſuperatur, tum pari gradu iter egerunt ſub
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>.t.i.</
var
>
quo ſupra
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>
ambulauerant.
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</
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<
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xml:space
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">Hoc animaduertendo, quòd ſi ſumma progreſſionis maior eſſet rectangulo, ex ea
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ſumma neceſſe eſſet
<
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mil
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liarium vltimi termini in ſumma
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<
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xlink:href
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incluſi detrahere, & reſiduo ope-
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rari. </
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<
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xml:space
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">Nunc verò ſummam pro-
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greſſionis exſumma rectanguli à
<
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primo viatore facti ſubtrahi de-
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bet,
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ſeruari
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