v2 = r2 - byy : c wie im ersten Falle
III. Es sey yy - dxy : f = aa - bxx : c
Nehmet wie vorhin das andere Glied d
xy : f weg. Setzet nemlich
y = v + dx : 2f
so ist y2 = v2 + dxv : f + d2x2 : 4 f2
-dxy : f = - dxv : f - d2x2 : 2f2
v2 - dx2 : 4f2 = aa - bxx : c
v2 = aa - bx2 : c + d2x2 : 4ff.
das ist v2 -- aa - (4bffx2 + cd2x2) : 4ffc
Setzet ferner -4bff + cdd = m/ 4ffc = n
so ist v2 = aa - mx2 : n/ wie im ersten
Falle.
IV. Es sey yy + dxy : f = ax - bxx : c. Neh-
met abermal das andere Glied dxy : s
weg. Setzet nemlich
y = v - dx : 2f
so ist y2 = v2 - dxv : f + d2x2 : 4f2
+ dxy : f = + dxv : f - d2 x2: 2f2
v2 - d2 x2 : 4f2 = ax - bxx : c
v2 = ax + d2 x2 : 4f2 - bx2 : c
das ist/ v2 = ax + (d2cx2 - 4bf2 x2) : 4cf2
Setzet ferner d2 c - 4bf2 = m/ 4cf2 = n
so ist v2 = ax - mx2 : n
oder
O 3
v2 = r2 - byy : c wie im erſten Falle
III. Es ſey yy - dxy : f = aa - bxx : c
Nehmet wie vorhin das andere Glied d
xy : f weg. Setzet nemlich
y = v + dx : 2f
ſo iſt y2 = v2 + dxv : f + d2x2 : 4 f2
-dxy : f = - dxv : f - d2x2 : 2f2
v2 - dx2 : 4f2 = aa - bxx : c
v2 = aa - bx2 : c + d2x2 : 4ff.
das iſt v2 — aa - (4bffx2 + cd2x2) : 4ffc
Setzet ferner -4bff + cdd = m/ 4ffc = n
ſo iſt v2 = aa - mx2 : n/ wie im erſten
Falle.
IV. Es ſey yy + dxy : f = ax - bxx : c. Neh-
met abermal das andere Glied dxy : ſ
weg. Setzet nemlich
y = v - dx : 2f
ſo iſt y2 = v2 - dxv : f + d2x2 : 4f2
+ dxy : f = + dxv : f - d2 x2: 2f2
v2 - d2 x2 : 4f2 = ax - bxx : c
v2 = ax + d2 x2 : 4f2 - bx2 : c
das iſt/ v2 = ax + (d2cx2 - 4bf2 x2) : 4cf2
Setzet ferner d2 c - 4bf2 = m/ 4cf2 = n
ſo iſt v2 = ax - mx2 : n
oder
O 3
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<item><pb facs="#f0215" n="213"/><fw place="top" type="header"><hi rendition="#b">der Algebra.</hi></fw><lb/><hi rendition="#aq"><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">r</hi><hi rendition="#sup">2</hi> - <hi rendition="#i">byy : c</hi></hi> wie im erſten Falle</item><lb/>
<item><hi rendition="#aq">III.</hi> Es ſey <hi rendition="#aq"><hi rendition="#i">yy - dxy</hi> : f = <hi rendition="#i">aa - bxx : c</hi></hi><lb/>
Nehmet wie vorhin das andere Glied <hi rendition="#aq"><hi rendition="#i">d<lb/>
xy</hi> : f</hi> weg. Setzet nemlich<lb/><hi rendition="#aq"><hi rendition="#u"><hi rendition="#i">y = v + dx</hi> : 2f</hi></hi><lb/>
ſo iſt <hi rendition="#aq"><hi rendition="#i">y</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">v</hi><hi rendition="#sup">2</hi> + <hi rendition="#i">dxv</hi> : <hi rendition="#i">f</hi> + <hi rendition="#i">d</hi><hi rendition="#sup">2</hi><hi rendition="#i">x</hi><hi rendition="#sup">2</hi> : 4 <hi rendition="#i">f</hi><hi rendition="#sup">2</hi><lb/><hi rendition="#u"><hi rendition="#i">-dxy</hi> : <hi rendition="#i">f</hi> = - <hi rendition="#i">dxv</hi> : <hi rendition="#i">f</hi> - <hi rendition="#i">d</hi><hi rendition="#sup">2</hi>x<hi rendition="#sup">2</hi> : 2<hi rendition="#i">f</hi><hi rendition="#sup">2</hi><lb/><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> - <hi rendition="#i">dx</hi><hi rendition="#sup">2</hi> : 4<hi rendition="#i">f</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">aa - bxx</hi> : <hi rendition="#i">c</hi></hi><lb/><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">aa - bx</hi><hi rendition="#sup">2</hi> : <hi rendition="#i">c + d</hi><hi rendition="#sup">2</hi><hi rendition="#i">x</hi><hi rendition="#sup">2</hi> : 4<hi rendition="#i">ff.</hi></hi><lb/>
das iſt <hi rendition="#aq"><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> — <hi rendition="#i">aa</hi> - (4<hi rendition="#i">bffx</hi><hi rendition="#sup">2</hi> + <hi rendition="#i">cd</hi><hi rendition="#sup">2</hi><hi rendition="#i">x</hi><hi rendition="#sup">2</hi>) : 4<hi rendition="#i">ffc</hi></hi><lb/>
Setzet ferner -4<hi rendition="#aq"><hi rendition="#i">bff + cdd = m/</hi> 4<hi rendition="#i">ffc = n</hi></hi><lb/>
ſo iſt <hi rendition="#aq"><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">aa - mx</hi><hi rendition="#sup">2</hi> : <hi rendition="#i">n/</hi></hi> wie im erſten<lb/>
Falle.</item><lb/>
<item><hi rendition="#aq">IV.</hi> Es ſey <hi rendition="#aq"><hi rendition="#i">yy + dxy : f = ax - bxx : c.</hi></hi> Neh-<lb/>
met abermal das andere Glied <hi rendition="#aq"><hi rendition="#i">dxy : ſ</hi></hi><lb/>
weg. Setzet nemlich<lb/><hi rendition="#aq"><hi rendition="#u"><hi rendition="#i">y = v - dx</hi> : 2<hi rendition="#i">f</hi></hi></hi><lb/>
ſo iſt <hi rendition="#aq"><hi rendition="#i">y</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">v</hi><hi rendition="#sup">2</hi> - <hi rendition="#i">dxv</hi> : <hi rendition="#i">f + d</hi><hi rendition="#sup">2</hi><hi rendition="#i">x</hi><hi rendition="#sup">2</hi> : 4<hi rendition="#i">f</hi><hi rendition="#sup">2</hi><lb/><hi rendition="#u">+ <hi rendition="#i">dxy</hi> : <hi rendition="#i">f</hi> = + <hi rendition="#i">dxv</hi> : <hi rendition="#i">f - d</hi><hi rendition="#sup">2</hi> <hi rendition="#i">x</hi><hi rendition="#sup">2</hi>: 2<hi rendition="#i">f</hi><hi rendition="#sup">2</hi><lb/><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> - <hi rendition="#i">d</hi><hi rendition="#sup">2</hi> <hi rendition="#i">x</hi><hi rendition="#sup">2</hi> : 4<hi rendition="#i">f</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">ax - bxx</hi> : <hi rendition="#i">c</hi></hi><lb/><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">ax + d</hi><hi rendition="#sup">2</hi> <hi rendition="#i">x</hi><hi rendition="#sup">2</hi> : 4<hi rendition="#i">f</hi><hi rendition="#sup">2</hi> - <hi rendition="#i">bx</hi><hi rendition="#sup">2</hi> : <hi rendition="#i">c</hi></hi><lb/>
das iſt/ <hi rendition="#aq"><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">ax</hi> + (<hi rendition="#i">d</hi>2<hi rendition="#i">cx</hi><hi rendition="#sup">2</hi> - 4<hi rendition="#i">bf</hi><hi rendition="#sup">2</hi> <hi rendition="#i">x</hi><hi rendition="#sup">2</hi>) : 4<hi rendition="#i">cf</hi><hi rendition="#sup">2</hi></hi><lb/>
Setzet ferner <hi rendition="#aq"><hi rendition="#i">d</hi><hi rendition="#sup">2</hi><hi rendition="#i">c</hi> - 4<hi rendition="#i">bf</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">m/</hi> 4<hi rendition="#i">cf</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">n</hi></hi><lb/>
ſo iſt <hi rendition="#aq"><hi rendition="#u"><hi rendition="#i">v</hi><hi rendition="#sup">2</hi> = <hi rendition="#i">ax - mx</hi><hi rendition="#sup">2</hi> : <hi rendition="#i">n</hi></hi></hi><lb/>
<fw place="bottom" type="sig">O 3</fw><fw place="bottom" type="catch">oder</fw><lb/></item>
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[213/0215]
der Algebra.
v2 = r2 - byy : c wie im erſten Falle
III. Es ſey yy - dxy : f = aa - bxx : c
Nehmet wie vorhin das andere Glied d
xy : f weg. Setzet nemlich
y = v + dx : 2f
ſo iſt y2 = v2 + dxv : f + d2x2 : 4 f2
-dxy : f = - dxv : f - d2x2 : 2f2
v2 - dx2 : 4f2 = aa - bxx : c
v2 = aa - bx2 : c + d2x2 : 4ff.
das iſt v2 — aa - (4bffx2 + cd2x2) : 4ffc
Setzet ferner -4bff + cdd = m/ 4ffc = n
ſo iſt v2 = aa - mx2 : n/ wie im erſten
Falle.
IV. Es ſey yy + dxy : f = ax - bxx : c. Neh-
met abermal das andere Glied dxy : ſ
weg. Setzet nemlich
y = v - dx : 2f
ſo iſt y2 = v2 - dxv : f + d2x2 : 4f2
+ dxy : f = + dxv : f - d2 x2: 2f2
v2 - d2 x2 : 4f2 = ax - bxx : c
v2 = ax + d2 x2 : 4f2 - bx2 : c
das iſt/ v2 = ax + (d2cx2 - 4bf2 x2) : 4cf2
Setzet ferner d2 c - 4bf2 = m/ 4cf2 = n
ſo iſt v2 = ax - mx2 : n
oder
O 3