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Wolff, Christian von: Der Anfangs-Gründe Aller Mathematischen Wiessenschaften. Bd. 4. Halle (Saale), 1710.

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der Algebra.
x4 = h4x4 + 4h3ix5 + 6h2i2u6. &c.
+ 4h3k
x5 = h5a5 + 5h4iu6 &c.
x6 = h6u6 &c.

Setzet in der AEquation 0=-u + ax + bx2
+ cx3 + dx4 + ex5 + fx6 &c.
die gefundenenen
Werthe von x/ x2/ x3 &c. so bekommet ihr
- u = -u
+ ax =+ ahu+ aiu2+ aku3+ alu4+ amu5+ anu6
+ bx2 =+ bh2..+ 2bhi..+ bi2..+ 2bhl..+ bk2..
+ 2bhk..+ 2bik..+ 2bhm..
+ 2il..
+ cx3 =+ ch3..+ 3ch2i.+ 2chi2..+ 3ch2l..
+ 3cl2k..+ 6chik..
+ dx4+ ci3..
+ dh4..+ 4dh3i.+ 6dh2i2..
+ 4dh3k..
+ ex5 =+ eh5..+ 5eh4i..
+ fx6 =+ fh6..

Se-
U 3

der Algebra.
x4 = h4x4 + 4h3ix5 + 6h2i2u6. &c.
+ 4h3k
x5 = h5a5 + 5h4iu6 &c.
x6 = h6u6 &c.

Setzet in der Æquation 0=-u + ax + bx2
+ cx3 + dx4 + ex5 + fx6 &c.
die gefundenenen
Werthe von x/ x2/ x3 &c. ſo bekommet ihr
- u = -u
+ ax =+ ahu+ aiu2+ aku3+ alu4+ amu5+ anu6
+ bx2 =+ bh2..+ 2bhi..+ bi2..+ 2bhl..+ bk2..
+ 2bhk..+ 2bik..+ 2bhm..
+ 2il..
+ cx3 =+ ch3..+ 3ch2i.+ 2chi2..+ 3ch2l..
+ 3cl2k..+ 6chik..
+ dx4+ ci3..
+ dh4..+ 4dh3i.+ 6dh2i2..
+ 4dh3k..
+ ex5 =+ eh5..+ 5eh4i..
+ fx6 =+ fh6..

Se-
U 3
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                <p><pb facs="#f0311" n="309"/><fw place="top" type="header"><hi rendition="#b">der Algebra.</hi></fw><lb/><hi rendition="#aq"><hi rendition="#i">x</hi><hi rendition="#sup">4</hi> = <hi rendition="#i">h</hi><hi rendition="#sup">4</hi><hi rendition="#i">x</hi><hi rendition="#sup">4</hi> + 4<hi rendition="#i">h</hi><hi rendition="#sup">3</hi><hi rendition="#i">ix</hi><hi rendition="#sup">5</hi> + 6<hi rendition="#i">h</hi><hi rendition="#sup">2</hi><hi rendition="#i">i</hi><hi rendition="#sup">2</hi><hi rendition="#i">u</hi><hi rendition="#sup">6</hi>. &amp;c.</hi><lb/><hi rendition="#et"><hi rendition="#aq">+ 4<hi rendition="#i">h</hi><hi rendition="#sup">3</hi><hi rendition="#i">k</hi></hi></hi><lb/><hi rendition="#aq"><hi rendition="#i">x</hi><hi rendition="#sup">5</hi> = <hi rendition="#i">h</hi><hi rendition="#sup">5</hi><hi rendition="#i">a</hi><hi rendition="#sup">5</hi> + 5<hi rendition="#i">h</hi><hi rendition="#sup">4</hi><hi rendition="#i">iu</hi><hi rendition="#sup">6</hi> &amp;c.<lb/><hi rendition="#i">x</hi><hi rendition="#sup">6</hi> = <hi rendition="#i">h</hi><hi rendition="#sup">6</hi><hi rendition="#i">u</hi><hi rendition="#sup">6</hi> &amp;c.</hi><lb/>
Setzet in der <hi rendition="#aq">Æquation <hi rendition="#i">0=-u + ax + bx</hi><hi rendition="#sup">2</hi><lb/>
+ <hi rendition="#i">cx</hi><hi rendition="#sup">3</hi> + <hi rendition="#i">dx</hi><hi rendition="#sup">4</hi> + <hi rendition="#i">ex</hi><hi rendition="#sup">5</hi> + <hi rendition="#i">fx</hi><hi rendition="#sup">6</hi> &amp;c.</hi> die gefundenenen<lb/>
Werthe von <hi rendition="#aq">x/ x<hi rendition="#sup">2</hi>/ <hi rendition="#i">x</hi><hi rendition="#sup">3</hi> &amp;c.</hi> &#x017F;o bekommet ihr<lb/><table><row><cell><hi rendition="#aq"><hi rendition="#i">- u = -u</hi></hi></cell><cell/><cell/><cell/><cell/><cell/><cell/></row><lb/><row><cell>+ <hi rendition="#aq"><hi rendition="#i">ax</hi></hi> =</cell><cell>+ <hi rendition="#aq"><hi rendition="#i">ahu</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">aiu</hi><hi rendition="#sup">2</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">aku</hi><hi rendition="#sup">3</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">alu</hi><hi rendition="#sup">4</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">amu</hi><hi rendition="#sup">5</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">anu</hi><hi rendition="#sup">6</hi></hi></cell></row><lb/><row><cell>+ <hi rendition="#aq"><hi rendition="#i">bx</hi><hi rendition="#sup">2</hi></hi> =</cell><cell/><cell>+ <hi rendition="#aq"><hi rendition="#i">bh</hi><hi rendition="#sup">2</hi>..</hi></cell><cell>+ 2<hi rendition="#aq"><hi rendition="#i">bhi..</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">bi</hi><hi rendition="#sup">2</hi>..</hi></cell><cell>+ 2<hi rendition="#aq"><hi rendition="#i">bhl..</hi></hi></cell><cell>+ <hi rendition="#aq"><hi rendition="#i">bk</hi><hi rendition="#sup">2</hi>..</hi></cell></row><lb/><row><cell/><cell/><cell/><cell/><cell>+ 2<hi rendition="#aq"><hi rendition="#i">bhk..</hi></hi></cell><cell>+ 2<hi rendition="#aq"><hi rendition="#i">bik..</hi></hi></cell><cell>+ 2<hi rendition="#aq"><hi rendition="#i">bhm..</hi></hi></cell></row><lb/><row><cell/><cell/><cell/><cell/><cell/><cell/><cell>+ 2<hi rendition="#aq"><hi rendition="#i">il..</hi></hi></cell></row><lb/><row><cell>+ <hi rendition="#aq"><hi rendition="#i">cx</hi><hi rendition="#sup">3</hi></hi> =</cell><cell/><cell/><cell>+ <hi rendition="#aq"><hi rendition="#i">ch</hi><hi rendition="#sup">3</hi>..</hi></cell><cell>+ 3<hi rendition="#aq"><hi rendition="#i">ch</hi><hi rendition="#sup">2</hi><hi rendition="#i">i.</hi></hi></cell><cell>+ 2<hi rendition="#aq"><hi rendition="#i">chi</hi><hi rendition="#sup">2</hi>..</hi></cell><cell>+ 3<hi rendition="#aq"><hi rendition="#i">ch</hi><hi rendition="#sup">2</hi><hi rendition="#i">l..</hi></hi></cell></row><lb/><row><cell/><cell/><cell/><cell/><cell/><cell>+ 3<hi rendition="#aq"><hi rendition="#i">cl</hi><hi rendition="#sup">2</hi><hi rendition="#i">k..</hi></hi></cell><cell>+ 6<hi rendition="#aq"><hi rendition="#i">chik..</hi></hi></cell></row><lb/><row><cell>+ <hi rendition="#aq"><hi rendition="#i">dx</hi><hi rendition="#sup">4</hi></hi></cell><cell/><cell/><cell/><cell/><cell/><cell>+ <hi rendition="#aq"><hi rendition="#i">ci</hi><hi rendition="#sup">3</hi>..</hi></cell></row><lb/><row><cell/><cell/><cell/><cell/><cell>+ <hi rendition="#aq"><hi rendition="#i">dh</hi><hi rendition="#sup">4</hi>..</hi></cell><cell>+ 4<hi rendition="#aq"><hi rendition="#i">dh</hi><hi rendition="#sup">3</hi><hi rendition="#i">i.</hi></hi></cell><cell>+ 6<hi rendition="#aq"><hi rendition="#i">dh</hi><hi rendition="#sup">2</hi><hi rendition="#i">i</hi><hi rendition="#sup">2</hi>..</hi></cell></row><lb/><row><cell/><cell/><cell/><cell/><cell/><cell/><cell>+ 4<hi rendition="#aq"><hi rendition="#i">dh</hi><hi rendition="#sup">3</hi><hi rendition="#i">k..</hi></hi></cell></row><lb/><row><cell>+ <hi rendition="#aq"><hi rendition="#i">ex</hi><hi rendition="#sup">5</hi></hi> =</cell><cell/><cell/><cell/><cell/><cell>+ <hi rendition="#aq"><hi rendition="#i">eh</hi><hi rendition="#sup">5</hi>..</hi></cell><cell>+ 5<hi rendition="#aq"><hi rendition="#i">eh</hi><hi rendition="#sup">4</hi><hi rendition="#i">i..</hi></hi></cell></row><lb/><row><cell>+ <hi rendition="#aq"><hi rendition="#i">fx</hi><hi rendition="#sup">6</hi></hi> =</cell><cell/><cell/><cell/><cell/><cell/><cell>+ <hi rendition="#aq"><hi rendition="#i">fh</hi><hi rendition="#sup">6</hi>..</hi></cell></row></table><lb/>
<fw place="bottom" type="sig">U 3</fw><fw place="bottom" type="catch">Se-</fw><lb/></p>
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[309/0311] der Algebra. x4 = h4x4 + 4h3ix5 + 6h2i2u6. &c. + 4h3k x5 = h5a5 + 5h4iu6 &c. x6 = h6u6 &c. Setzet in der Æquation 0=-u + ax + bx2 + cx3 + dx4 + ex5 + fx6 &c. die gefundenenen Werthe von x/ x2/ x3 &c. ſo bekommet ihr - u = -u + ax = + ahu + aiu2 + aku3 + alu4 + amu5 + anu6 + bx2 = + bh2.. + 2bhi.. + bi2.. + 2bhl.. + bk2.. + 2bhk.. + 2bik.. + 2bhm.. + 2il.. + cx3 = + ch3.. + 3ch2i. + 2chi2.. + 3ch2l.. + 3cl2k.. + 6chik.. + dx4 + ci3.. + dh4.. + 4dh3i. + 6dh2i2.. + 4dh3k.. + ex5 = + eh5.. + 5eh4i.. + fx6 = + fh6.. Se- U 3

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Zitationshilfe: Wolff, Christian von: Der Anfangs-Gründe Aller Mathematischen Wiessenschaften. Bd. 4. Halle (Saale), 1710. , S. 309. In: Deutsches Textarchiv <https://www.deutschestextarchiv.de/wolff_anfangsgruende04_1710/311>, abgerufen am 29.04.2024.