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]

#### Table of figures

< >
[Figure 61]
[Figure 62]
[Figure 63]
[Figure 64]
[Figure 65]
[Figure 66]
[Figure 67]
[Figure 68]
[Figure 69]
[Figure 70]
[Figure 71]
[Figure 72]
[Figure 73]
[Figure 74]
[Figure 75]
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
[Figure 81]
[Figure 82]
[Figure 83]
[Figure 84]
[Figure 85]
[Figure 86]
[Figure 87]
[Figure 88]
[Figure 89]
[Figure 90]
< >
page |< < (34) of 445 > >|
<echo version="1.0">
<text type="book" xml:lang="la">
<div xml:id="echoid-div7" type="body" level="1" n="1">
<div xml:id="echoid-div7" type="chapter" level="2" n="1">
<div xml:id="echoid-div109" type="math:theorem" level="3" n="52">
<p>
<s xml:id="echoid-s455" xml:space="preserve">11. dabuntur .110. quo producto multiplicato cum .12. dabuntur .1320. hoc pro
<lb/>
ueniens per primum nempe .10. diuiſum dabit .132. numerum æqualem producto
<lb/>
ſecundi in tertium numerorum propoſitorum, ſcilicet .132.</s>
</p>
<p>
<s xml:id="echoid-s456" xml:space="preserve">Hoc vt ſpeculemur, primus numerus ſignificetur line
<var>a.o.u.</var>
ſecundus
<var>.e.o.</var>
tertius
<var>.
<lb/>
e.a.</var>
productum verò
<var>.o.u.</var>
in
<var>.o.e.</var>
ſit
<var>.o.i.</var>
ipſius ve
<lb/>
<var>.o.i.</var>
per
<var>.e.a.</var>
<reg norm="productum" type="context">productũ</reg>
<reg norm="corporeum" type="context">corporeũ</reg>
ſit
<var>.i.c.</var>
tum
<lb/>
</figure>
<reg norm="productum" type="context">productũ</reg>
<var>.e.o.</var>
in
<var>.e.a.</var>
ſit
<var>.e.c</var>
. </s>
<s xml:id="echoid-s457" xml:space="preserve">Dico
<reg norm="nunc" type="context">nũc</reg>
quod di-
<lb/>
uiſo numero corporeo
<var>.i.c.</var>
per
<reg norm="primum" type="context">primũ</reg>
<var>.o.u.</var>
<reg norm="proue" type="simple">ꝓue</reg>
<lb/>
niens æquale erit numero producti
<var>.e.c</var>
. </s>
<s xml:id="echoid-s458" xml:space="preserve">Qua-
<lb/>
re in primis cogitandum eſt, quod cum produ-
<lb/>
ctum
<var>.i.c.</var>
ortum fuerit ex multiplicatione
<var>.o.i.</var>
<lb/>
in
<var>.e.a</var>
: dictum
<var>.o.i.</var>
toties ingredietur
<var>.i.c.</var>
quo-
<lb/>
ties vnitas reperitur in
<var>.e.a.</var>
<lb/>
ties
<var>.e.c.</var>
in
<var>.i.c.</var>
quot vnitates erunt in
<var>.o.u</var>
. </s>
<s xml:id="echoid-s459" xml:space="preserve">
<reg norm="Itaque" type="simple">Itaq;</reg>
<lb/>
ſequitur quòd diuiſo
<var>.i.c.</var>
per
<var>o.u.</var>
proueniens ſit
<lb/>
<var>e.c.</var>
corporeum, æquale nihilominus producto
<var>.e.c.</var>
ſuperficiali.</s>
</p>
</div>
<div xml:id="echoid-div111" type="math:theorem" level="3" n="53">
<num value="53">LIII</num>
<p>
<s xml:id="echoid-s460" xml:space="preserve">CVR diuidens propoſitum numerum in tres partes ſic ſe habentes vt produ-
<lb/>
ctum primi in ſecundam, in tertia
<reg norm="multiplicatum" type="context">multiplicatũ</reg>
, præbeat numerum alteri nu-
<lb/>
mero propoſito æqualem. </s>
<s xml:id="echoid-s461" xml:space="preserve">Rectè ſecundum numerum per quemcunque alium mino
<lb/>
rem primo diuidit, qui diuidens vna erit ex tribus partibus quæſitis, proueniens
<lb/>
autem erit productum vnius in alteram reliquarum duarum, quarum ſumma cogni
<lb/>
ta erit, detracto numero diuidente ex primo dato, quam quidem ſi diſtinguere
<lb/>
quis voluerit, vtetur theoremate .45.</s>
</p>
<p>
<s xml:id="echoid-s462" xml:space="preserve">Exempli gratia, proponitur numerus .20. in tres partes diuidendus, quæ ſic ſe
<lb/>
habeant, ut productum primæ in ſecundam in tertia multiplicatum det .90. itaque
<lb/>
ſumenda erit pro prima vna pars ipſius .20. quæcunque illa ſit, verbi gratia .2. qua
<lb/>
ſecundus numerus, nempe .90. diuidatur, dabitur igitur .45. quod erit productum
<lb/>
cæterarum partium inter ſe, quarum ſumma eſt .18. quam ſummam ſi diſtinguere
<lb/>
volueris in cęteris duabus partibus ſeparatis, vteris .45. theoremate, vt quàm citiſ-
<lb/>
ſimè quod cupis exequaris, erunt autem partes .3. et .15.</s>
</p>
<p>
<s xml:id="echoid-s463" xml:space="preserve">In cuius ſpeculationis gratiam nihil aliud occurrit, quàm quod præcedenti theo-
<lb/>
remate, & ſuperiore .45. allatum eſt.</s>
</p>
</div>
<div xml:id="echoid-div112" type="math:theorem" level="3" n="54">
<num value="54">LIIII</num>
<p>
<s xml:id="echoid-s464" xml:space="preserve">
<emph style="sc">DIvidere</emph>
numerum in .3. eiuſmodi partes, vt quadratum vnius ſit æquale
<lb/>
producto reliquarum duarum inter ſe, idem omnino eſt cum 51. theoremate.
<lb/>
</s>
<s xml:id="echoid-s465" xml:space="preserve">Nam qui ſumet quamlibet partem propoſiti numeri, quæ tertia parte maior tamen
<lb/>
non ſit,
<reg norm="reſiduumque" type="simple">reſiduumq́</reg>
in duas tales partes diuiſerit, vt prima ſumpta, media proportio
<lb/>
nalis ſit ex probatione .51. theoremate allata, propoſitum conſequetur.</s>
</p>
</div>
<div xml:id="echoid-div113" type="math:theorem" level="3" n="55">
<num value="55">LV</num>