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< | <head>Memoranda</head> | ||
the angles of Triangles</note><lb/> | <!-- Everything on this page is crossed through but legible. --> | ||
<note>Cor. concerning<lb/> | |||
the angles of Triangles<lb/><!-- Red Ink -->DEMONSTRAN</note> | |||
<p>Let there be a Corrollary to some Prop. Declaring that<lb/> | |||
a Triangle cannot have more than one obtuse angle, <lb/> | a Triangle cannot have more than one obtuse angle, <lb/> | ||
also that a Triangle cannot have more than one right | also that a Triangle cannot have more than one right <lb/> | ||
angle from which it will follow that every Triangle<lb/> | angle from which it will follow that every Triangle<lb/> | ||
must have 2 acute angles. These may be given for<lb/> | must have 2 acute angles. These may be given for<lb/> | ||
the reason for calling | the reason for calling those Triangles that have, one<lb/> | ||
right angle <hi rend="underline">right angled</hi>, those that have one obtuse, <lb/> | right angle <hi rend="underline">right angled</hi>, those that have one obtuse, <lb/> | ||
<hi rend="underline">obtuse angled</hi> and those that have three acute,<lb/> | <hi rend="underline">obtuse angled</hi> and those that have three acute,<lb/> | ||
<hi rend="underline">acute angled</hi>.</p> <pb/> | <hi rend="underline">acute angled</hi>.</p> <pb/> | ||
<note>Description vice<lb/> | <note>Description vice<lb/> | ||
Definition.</note> | |||
<p>Where a definition can not be had we must be content<lb/> | |||
with a description.</p> | with a description.</p> | ||
<note><!-- Red ink -->Demonstranda</note> | |||
<note><!-- Red ink -->Demonstranda</note> | |||
<note>Cor. concerning<lb/> | |||
the <sic>exteriour</sic> angles<lb/> | the <sic>exteriour</sic> angles<lb/> | ||
of a Square.</note> If the sides of a square< | of a Square.</note> | ||
<p> If the sides of a square <add>any square angled Figure</add> be produced the <add><sic>exteriour</sic></add> angles which <del>they</del><lb/> | |||
the produced parts make with each other shall be right angles.</p> | the produced parts make with each other shall be right angles.</p> | ||
<note><!-- Red Ink -->Demonstranda</note> | |||
Method of</note> | <note>New Prop.</note> | ||
<p> A Figure must have as many sides as it has angles and<lb/> | |||
vice versa</p> | |||
<note>Description<lb/> | |||
Method of</note> | |||
<p>In description of species of Figures first state the<lb/> | |||
several <del>diff</del> <gap/> that can happen determining<lb/> | several <del>diff</del> <gap/> that can happen determining<lb/> | ||
the species and then give names to each.</p> | the species and then give names to each.</p> | ||
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enumerated</note> When a Term is defined write all those that are synonimous<lb/> | enumerated</note> When a Term is defined write all those that are synonimous<lb/> | ||
which are used by any Geometrician.</p> | which are used by any Geometrician.</p> | ||
<note><!-- Red ink -->Definienda</note><lb/> | |||
<note><!-- Red ink -->Definienda</note> | |||
<note>Oblique Triangles<lb/> | |||
Defin: of.</note> | |||
<p>Oblique Triangles are such as have no right angle<lb/> | <p>Oblique Triangles are such as have no right angle<lb/> | ||
the species of these are acute <del>or</del><add>and</add> obtuse.<lb/> | |||
<unclear>N3</unclear> equilateral Triangles need be acute.</p> | |||
<unclear> | |||
<note>More regular<lb/> | <note>More regular<lb/> | ||
right | right lined Figures</note> | ||
<p>Many other right lined figures may be called<lb/> | |||
regular besides those mentioned by Euclid<lb/> | |||
for example the opposite boundaries of a trapezium<lb/> | for example the opposite boundaries of a trapezium<lb/> | ||
may be equal and yet not parallel<lb/> | may be equal and yet not parallel<lb/> | ||
<del>but</del><add>and</add> in such figures the angles | <del>but</del><add>and</add> in such figures the angles |^^^| at the correspondent<lb/> | ||
ends of opposite boundaries may be equal or &c.< | ends of opposite boundaries may be equal or &c.</p> | ||
<note>Trapezium<lb/> | <note>Trapezium<lb/> | ||
Genus<lb/> | Genus<lb/> | ||
Parallelogram<lb/> | Parallelogram<lb/> | ||
Species.</note> Trapezium should be the highest Genus of all<lb/> | Species.</note> | ||
<p> Trapezium should be the highest Genus of all<lb/> | |||
four sided figures Parallelogram a Species<lb/> | four sided figures Parallelogram a Species<lb/> | ||
rectangle rhombus | rectangle, rhombus &c a species of parallelogram.</p> | ||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}}{{Completed}} | ||
Memoranda
Cor. concerning
the angles of Triangles
DEMONSTRAN
Let there be a Corrollary to some Prop. Declaring that
a Triangle cannot have more than one obtuse angle,
also that a Triangle cannot have more than one right
angle from which it will follow that every Triangle
must have 2 acute angles. These may be given for
the reason for calling those Triangles that have, one
right angle right angled, those that have one obtuse,
obtuse angled and those that have three acute,
acute angled.
---page break---
Description vice
Definition.
Where a definition can not be had we must be content
with a description.
Demonstranda
Cor. concerning
the exteriour angles
of a Square.
If the sides of a square any square angled Figure be produced the exteriour angles which they
the produced parts make with each other shall be right angles.
Demonstranda
New Prop.
A Figure must have as many sides as it has angles and
vice versa
Description
Method of
In description of species of Figures first state the
several diff that can happen determining
the species and then give names to each.
Synonimous terms
enumerated When a Term is defined write all those that are synonimous
which are used by any Geometrician.
Definienda
Oblique Triangles
Defin: of.
Oblique Triangles are such as have no right angle
the species of these are acute orand obtuse.
N3 equilateral Triangles need be acute.
More regular
right lined Figures
Many other right lined figures may be called
regular besides those mentioned by Euclid
for example the opposite boundaries of a trapezium
may be equal and yet not parallel
butand in such figures the angles |^^^| at the correspondent
ends of opposite boundaries may be equal or &c.
Trapezium
Genus
Parallelogram
Species.
Trapezium should be the highest Genus of all
four sided figures Parallelogram a Species
rectangle, rhombus &c a species of parallelogram.
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sir samuel bentham |
[[watermarks::gr [with crown] [britannia motif]]] |
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