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<head>Book the Six</head><p><head>Prop I Theor</head>Triangles and parallelograms of<lb/>the same altitude are to one<lb/>another as their bases —</p>-----<p><head>Prop VII Theor --</head>If two triangles have one angle of the one equal to<lb/>one angle of the other, and the sides about two other<lb/>angles proportionals: then if each of the<lb/>remaining angles be either less or not less<lb/>than a right angle, or if one of them be a<lb/>right angle the triangle shall be equiangular<lb/>and have those angles equal about which the<lb/>sides are proportionals.</p>-----<p><head>Prop XIV Theor -</head>Equal parallelograms which have<lb/>one angle of the one equal to one angle<lb/>of the other, have their Sides about the<lb/>equal angles reciprocally proportional,<lb/>and parallelograms that have one angle<lb/>of the one equal to one of the other<lb/>and their sides about their equal angle<lb/>reciprocally proportional, are equal to<lb/>one another.</p>-----<p><head>Prop XXI Theor.</head>Rectilineal figures which are<lb/>similar to the same rectilineal<lb/>figure, are also similar to one<lb/>another.</p>-----<p><head>Prop XXVIII Prob --</head>To a given straight line to apply a<lb/>parallelogram equal to a given rectilineal<lb/>figure and deficient by a parallelogram<lb/>similar to a given parallelogram but the<lb/>given rectilineal figure to which the<lb/>parallelogram to be applied <add>is</add> to be equal<lb/>must not be greater than the parallelogram<lb/>applied to half of the given line,<lb/>having its defect similar to the defect of<lb/>that which is to be applied: that is to<lb/>-----<lb/>the given parallelogram —</p><p><head>Prop C Theor.</head> If from an angle of<lb/>a triangle a <sic>strait</sic> line be drawn<lb/>perpendicular to the base: the rectangle<lb/>contained by the sides of the triangle is<lb/>equal to the rectangle contained by<lb/>the perpendicular and the diameter<lb/>of the circle described about the<lb/>triangle.</p> | <head>Book the Six</head><p><head>Prop I Theor</head>Triangles and parallelograms of<lb/>the same altitude are to one<lb/>another as their bases —</p>-----<p><head>Prop VII Theor --</head>If two triangles have one angle of the one equal to<lb/>one angle of the other, and the sides about two other<lb/>angles proportionals: then if each of the<lb/>remaining angles be either less or not less<lb/>than a right angle, or if one of them be a<lb/>right angle the triangle shall be equiangular<lb/>and have those angles equal about which the<lb/>sides are proportionals.</p>-----<p><head>Prop XIV Theor -</head>Equal parallelograms which have<lb/>one angle of the one equal to one angle<lb/>of the other, have their Sides about the<lb/>equal angles reciprocally proportional,<lb/>and parallelograms that have one angle<lb/>of the one equal to one of the other<lb/>and their sides about their equal angle<lb/>reciprocally proportional, are equal to<lb/>one another.</p>-----<p><head>Prop XXI Theor.</head>Rectilineal figures which are<lb/>similar to the same rectilineal<lb/>figure, are also similar to one<lb/>another.</p>-----<p><head>Prop XXVIII Prob --</head>To a given straight line to apply a<lb/>parallelogram equal to a given rectilineal<lb/>figure and deficient by a parallelogram<lb/>similar to a given parallelogram but the<lb/>given rectilineal figure to which the<lb/>parallelogram to be applied <add>is</add> to be equal<lb/>must not be greater than the parallelogram<lb/>applied to half of the given line,<lb/>having its defect similar to the defect of<lb/>that which is to be applied: that is to<lb/>-----<lb/>the given parallelogram —</p><p><head>Prop C Theor.</head> If from an angle of<lb/>a triangle a <sic>strait</sic> line be drawn<lb/>perpendicular to the base: the rectangle<lb/>contained by the sides of the triangle is<lb/>equal to the rectangle contained by<lb/>the perpendicular and the diameter<lb/>of the circle described about the<lb/>triangle.</p><pb/><p><head>Prop II Theor --</head>If a straight line be drawn parallel to<lb/>one of the Sides of a triangle, it shall<lb/>cut the other sides, or these produced,<lb/>proportionally. And if the sides, or the<lb/>sides roduced be cut proportionally,<lb/>the straight lines which <sic>joins</sic> the<lb/>point of Section shall be parallel to<lb/>the remaining side of the triangle.</p>-----<p><head>Prop VIII Theor --</head>In a right angled triangle, if a perpendicular<lb/>be drawn from the right angle to<lb/>the base: the triangles on each side of it<lb/>are similar to the whole triangle &<lb/>to one another</p>-----<p><head>Prop XV Theor --</head>Equal triangles which have one angle<lb/>of the one equal to one angle of the other,<lb/>have their Sides about the equal angles<lb/>reciprocally proportional: and triangles<lb/>which have one angle in the one<lb/>equal to one angle in the other and<lb/>their Sides about the equal angles<lb/>reciprocally proportional are equal to one another.</p> | ||
Book the Six
Prop I TheorTriangles and parallelograms of
the same altitude are to one
another as their bases —
-----
Prop VII Theor --If two triangles have one angle of the one equal to
one angle of the other, and the sides about two other
angles proportionals: then if each of the
remaining angles be either less or not less
than a right angle, or if one of them be a
right angle the triangle shall be equiangular
and have those angles equal about which the
sides are proportionals.
-----
Prop XIV Theor -Equal parallelograms which have
one angle of the one equal to one angle
of the other, have their Sides about the
equal angles reciprocally proportional,
and parallelograms that have one angle
of the one equal to one of the other
and their sides about their equal angle
reciprocally proportional, are equal to
one another.
-----
Prop XXI Theor.Rectilineal figures which are
similar to the same rectilineal
figure, are also similar to one
another.
-----
Prop XXVIII Prob --To a given straight line to apply a
parallelogram equal to a given rectilineal
figure and deficient by a parallelogram
similar to a given parallelogram but the
given rectilineal figure to which the
parallelogram to be applied is to be equal
must not be greater than the parallelogram
applied to half of the given line,
having its defect similar to the defect of
that which is to be applied: that is to
-----
the given parallelogram —
Prop C Theor. If from an angle of
a triangle a strait line be drawn
perpendicular to the base: the rectangle
contained by the sides of the triangle is
equal to the rectangle contained by
the perpendicular and the diameter
of the circle described about the
triangle.
---page break---
Prop II Theor --If a straight line be drawn parallel to
one of the Sides of a triangle, it shall
cut the other sides, or these produced,
proportionally. And if the sides, or the
sides roduced be cut proportionally,
the straight lines which joins the
point of Section shall be parallel to
the remaining side of the triangle.
-----
Prop VIII Theor --In a right angled triangle, if a perpendicular
be drawn from the right angle to
the base: the triangles on each side of it
are similar to the whole triangle &
to one another
-----
Prop XV Theor --Equal triangles which have one angle
of the one equal to one angle of the other,
have their Sides about the equal angles
reciprocally proportional: and triangles
which have one angle in the one
equal to one angle in the other and
their Sides about the equal angles
reciprocally proportional are equal to one another.
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Identifier: | JB/135/072/005"JB/" can not be assigned to a declared number type with value 135. |
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072 |
the propositions of the fifth and sixth books of euclid as expressed by simson those written with red ink are added by himself |
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005 |
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private material |
3 |
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recto |
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sir samuel bentham |
[[watermarks::[tall thin motif with prince of wales feathers] icv]] |
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46190 |
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