★ Find a new page to transcribe in our list of Untranscribed Manuscripts
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
<!-- ENTER TRANSCRIPTION BELOW THIS LINE --> | <!-- ENTER TRANSCRIPTION BELOW THIS LINE --> | ||
<head>Sixth</head><p>If the outward angle of<lb/>by producing one of its<lb/>into two equal angles<lb/>which also cuts the base<lb/>segments between the<lb/>and the extremeties of the<lb/>same ratio which the other<lb/>ngle have to one another. &<lb/>which the other sides of the tri<lb/>straight line drawn from<lb/>the point of sectional divide<lb/>-----<lb/>angle of the triangle into<lb/>gles —</p-----><p><head><del>Theor</del> -- Prob --</head>straight line similarly to<lb/>line, that is into parts<lb/>the same ratio to one<lb/>the parts of the divided<lb/>line have —</p>-----<p><head>XVII Theor --</head>ight lines be proportionals<lb/>contained by the extremes<lb/>square of the mean;<lb/>tangle contained by the<lb/>equal to the Square of the<lb/>aight lines are proportional.</p>-----<p><head>XIV Theor -</head>ams about the diameter<lb/>elogram, are similar<lb/>and to one another.</p>-----<p><head>XXXI Theor --</head>led triangles the rectili<lb/>described upon the side<lb/>the right angle is<lb/>similar and similarly<lb/>ures upon the sides<lb/>the right angle.</p><pb/><p><head>Prop IV Theor --</head>The sides about the equal angles of<lb/>equiangular triangles are proportionals;<lb/>and those which are opposite to the<lb/>equal angles are homologous sides<lb/>that is, are the antecedents or<lb/>consequents of the ratios —</p>-----<p><head>Prob XI Prob --</head>To find a third proportional to two<lb/>given straight lines</p>-----<p><head>Prop XVIII <del>Theor</del> -- Prob --</head>Upon a given straight line to describe<lb/>a rectilineal figure similar and<lb/>similarly situated to a given rectilineal<lb/>figure</p>-----<p><head>Prop XXV <del>Theor</del> Prob</head>To describe a rectilineal figure<lb/>which shall be similar to one<lb/>and equal to another given rectilineal<lb/>figure -</p>-----<p><head>Prop XXXII Theor --</head>If two triangles which have two Sides<lb/>of the one proportional to two sides of<lb/>the other, be joined at <add>one</add> <del>the</del> angle, so as<lb/>to have their homologous sides<lb/>parallel to one another, the remaining<lb/>sides shall be in a straight<lb/>line —</p><pb/><p><head>Prop V Theor</head>If the sides of two triangles, about each<lb/>of their angles be proportionals, the<lb/>triangles shall be equiangular and<lb/>shall have <add>their equal angles</add> <del>those angles equal which</del><lb/>opposite to the homologous sides</p>-----<p><head>Prop XII Prob</head>To find a fourth proportional to<lb/>three given straight lines</p>-----<p><head>Prop XIX Theor --</head>Similar triangles are to one<lb/>another in the duplicate ratio of<lb/>their homologous Sides —</p>-----<p><head>Prop XXVI Theor --</head>If two similar parallelograms<lb/>have a common angle and be<lb/>similarly situated: they are<lb/>about the same diameter —</p>-----<p><head>Prop XXXIII. Theor -</head>In equal Circles, Angles, whether at<lb/>the Centers or Circumferences, have<lb/>the same ratio which the Circumferences<lb/>on which they stand have<lb/>to one another. So also have the Sectors —</p><pb/><p><head>Prop VI Theor --</head>If two triangles have one angle of the one<lb/>equal to one angle of the other and the<lb/>sides about the equal angles proportionals,<lb/>the triangles shall be equiangular,<lb/>and shall have those angles equal<lb/>which are opposite to the homologous<lb/>sides —</p>-----<p><head>Prop XIII <del>Theor</del> -- Prob</head>To find a mean proportional between<lb/>two given straight lines —</p>-----<p><head>Prop XX. Theor --</head>Similar polygons may be divided into<lb/>the same number of similar <del>figures</del><lb/>triangles having the ratio to one<lb/>another that the polygons have:<lb/>and the polygons have to one another the<lb/>duplicate ratio of that which their<lb/>homologous sides have —</p>-----<p><head>Prop XXVII</head>Of all parallelograms applied to the Same<lb/>straight line, and deficient by<lb/>parallelograms similar and similarly<lb/>situated to that which is described upon<lb/>the half of the line: that which is applied<lb/>to the half, and is similar to its defect<lb/>is greatest. —</p>-----<p><head>Prop B. Theor</head>If an angle of a triangle be bisectio by<lb/>a straight line, which likewise cuts<lb/>the base: the rectangle contained<lb/>by the sides of the triangle is equal<lb/>to the rectangle contained by the<lb/>segments of the base, together with the<lb/>square of the straight line bisecting the angle.</p> | <!-- This page is formatted in rows with three paragraphs in each row. --><lb/><head>Sixth</head><p>If the outward angle of<lb/>by producing one of its<lb/>into two equal angles<lb/>which also cuts the base<lb/>segments between the<lb/>and the extremeties of the<lb/>same ratio which the other<lb/>ngle have to one another. &<lb/>which the other sides of the tri<lb/>straight line drawn from<lb/>the point of sectional divide<lb/>-----<lb/>angle of the triangle into<lb/>gles —</p-----><p><head><del>Theor</del> -- Prob --</head>straight line similarly to<lb/>line, that is into parts<lb/>the same ratio to one<lb/>the parts of the divided<lb/>line have —</p>-----<p><head>XVII Theor --</head>ight lines be proportionals<lb/>contained by the extremes<lb/>square of the mean;<lb/>tangle contained by the<lb/>equal to the Square of the<lb/>aight lines are proportional.</p>-----<p><head>XIV Theor -</head>ams about the diameter<lb/>elogram, are similar<lb/>and to one another.</p>-----<p><head>XXXI Theor --</head>led triangles the rectili<lb/>described upon the side<lb/>the right angle is<lb/>similar and similarly<lb/>ures upon the sides<lb/>the right angle.</p><pb/><p><head>Prop IV Theor --</head>The sides about the equal angles of<lb/>equiangular triangles are proportionals;<lb/>and those which are opposite to the<lb/>equal angles are homologous sides<lb/>that is, are the antecedents or<lb/>consequents of the ratios —</p>-----<p><head>Prob XI Prob --</head>To find a third proportional to two<lb/>given straight lines</p>-----<p><head>Prop XVIII <del>Theor</del> -- Prob --</head>Upon a given straight line to describe<lb/>a rectilineal figure similar and<lb/>similarly situated to a given rectilineal<lb/>figure</p>-----<p><head>Prop XXV <del>Theor</del> Prob</head>To describe a rectilineal figure<lb/>which shall be similar to one<lb/>and equal to another given rectilineal<lb/>figure -</p>-----<p><head>Prop XXXII Theor --</head>If two triangles which have two Sides<lb/>of the one proportional to two sides of<lb/>the other, be joined at <add>one</add> <del>the</del> angle, so as<lb/>to have their homologous sides<lb/>parallel to one another, the remaining<lb/>sides shall be in a straight<lb/>line —</p><pb/><p><head>Prop V Theor</head>If the sides of two triangles, about each<lb/>of their angles be proportionals, the<lb/>triangles shall be equiangular and<lb/>shall have <add>their equal angles</add> <del>those angles equal which</del><lb/>opposite to the homologous sides</p>-----<p><head>Prop XII Prob</head>To find a fourth proportional to<lb/>three given straight lines</p>-----<p><head>Prop XIX Theor --</head>Similar triangles are to one<lb/>another in the duplicate ratio of<lb/>their homologous Sides —</p>-----<p><head>Prop XXVI Theor --</head>If two similar parallelograms<lb/>have a common angle and be<lb/>similarly situated: they are<lb/>about the same diameter —</p>-----<p><head>Prop XXXIII. Theor -</head>In equal Circles, Angles, whether at<lb/>the Centers or Circumferences, have<lb/>the same ratio which the Circumferences<lb/>on which they stand have<lb/>to one another. So also have the Sectors —</p><pb/><p><head>Prop VI Theor --</head>If two triangles have one angle of the one<lb/>equal to one angle of the other and the<lb/>sides about the equal angles proportionals,<lb/>the triangles shall be equiangular,<lb/>and shall have those angles equal<lb/>which are opposite to the homologous<lb/>sides —</p>-----<p><head>Prop XIII <del>Theor</del> -- Prob</head>To find a mean proportional between<lb/>two given straight lines —</p>-----<p><head>Prop XX. Theor --</head>Similar polygons may be divided into<lb/>the same number of similar <del>figures</del><lb/>triangles having the ratio to one<lb/>another that the polygons have:<lb/>and the polygons have to one another the<lb/>duplicate ratio of that which their<lb/>homologous sides have —</p>-----<p><head>Prop XXVII</head>Of all parallelograms applied to the Same<lb/>straight line, and deficient by<lb/>parallelograms similar and similarly<lb/>situated to that which is described upon<lb/>the half of the line: that which is applied<lb/>to the half, and is similar to its defect<lb/>is greatest. —</p>-----<p><head>Prop B. Theor</head>If an angle of a triangle be bisectio by<lb/>a straight line, which likewise cuts<lb/>the base: the rectangle contained<lb/>by the sides of the triangle is equal<lb/>to the rectangle contained by the<lb/>segments of the base, together with the<lb/>square of the straight line bisecting the angle.</p> | ||
Sixth
If the outward angle of
by producing one of its
into two equal angles
which also cuts the base
segments between the
and the extremeties of the
same ratio which the other
ngle have to one another. &
which the other sides of the tri
straight line drawn from
the point of sectional divide
-----
angle of the triangle into
gles —</p----->
Theor -- Prob --straight line similarly to
line, that is into parts
the same ratio to one
the parts of the divided
line have —
-----
XVII Theor --ight lines be proportionals
contained by the extremes
square of the mean;
tangle contained by the
equal to the Square of the
aight lines are proportional.
-----
XIV Theor -ams about the diameter
elogram, are similar
and to one another.
-----
XXXI Theor --led triangles the rectili
described upon the side
the right angle is
similar and similarly
ures upon the sides
the right angle.
---page break---
Prop IV Theor --The sides about the equal angles of
equiangular triangles are proportionals;
and those which are opposite to the
equal angles are homologous sides
that is, are the antecedents or
consequents of the ratios —
-----
Prob XI Prob --To find a third proportional to two
given straight lines
-----
Prop XVIII Theor -- Prob --Upon a given straight line to describe
a rectilineal figure similar and
similarly situated to a given rectilineal
figure
-----
Prop XXV Theor ProbTo describe a rectilineal figure
which shall be similar to one
and equal to another given rectilineal
figure -
-----
Prop XXXII Theor --If two triangles which have two Sides
of the one proportional to two sides of
the other, be joined at one the angle, so as
to have their homologous sides
parallel to one another, the remaining
sides shall be in a straight
line —
---page break---
Prop V TheorIf the sides of two triangles, about each
of their angles be proportionals, the
triangles shall be equiangular and
shall have their equal angles those angles equal which
opposite to the homologous sides
-----
Prop XII ProbTo find a fourth proportional to
three given straight lines
-----
Prop XIX Theor --Similar triangles are to one
another in the duplicate ratio of
their homologous Sides —
-----
Prop XXVI Theor --If two similar parallelograms
have a common angle and be
similarly situated: they are
about the same diameter —
-----
Prop XXXIII. Theor -In equal Circles, Angles, whether at
the Centers or Circumferences, have
the same ratio which the Circumferences
on which they stand have
to one another. So also have the Sectors —
---page break---
Prop VI Theor --If two triangles have one angle of the one
equal to one angle of the other and the
sides about the equal angles proportionals,
the triangles shall be equiangular,
and shall have those angles equal
which are opposite to the homologous
sides —
-----
Prop XIII Theor -- ProbTo find a mean proportional between
two given straight lines —
-----
Prop XX. Theor --Similar polygons may be divided into
the same number of similar figures
triangles having the ratio to one
another that the polygons have:
and the polygons have to one another the
duplicate ratio of that which their
homologous sides have —
-----
Prop XXVIIOf all parallelograms applied to the Same
straight line, and deficient by
parallelograms similar and similarly
situated to that which is described upon
the half of the line: that which is applied
to the half, and is similar to its defect
is greatest. —
-----
Prop B. TheorIf an angle of a triangle be bisectio by
a straight line, which likewise cuts
the base: the rectangle contained
by the sides of the triangle is equal
to the rectangle contained by the
segments of the base, together with the
square of the straight line bisecting the angle.
|
Identifier: | JB/135/072/006"JB/" can not be assigned to a declared number type with value 135. |
|||
|---|---|---|---|
|
135 |
|||
|
072 |
the propositions of the fifth and sixth books of euclid as expressed by simson those written with red ink are added by himself |
||
|
006 |
|||
|
private material |
3 |
||
|
recto |
|||
|
sir samuel bentham |
[[watermarks::[tall thin motif with prince of wales feathers] icv]] |
||
|
46190 |
|||
