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<head>Books of Euclid as expressed by Simson. --</head><p><head>Theor.</head>be <sic>draw</sic> thro the Center of<lb/>raight line in it, which<lb/>the Center, it shall cut it<lb/>it cuts at right angles<lb/>it</p> | <head>Books of Euclid as expressed by Simson. --</head><p><head>Theor.</head>be <sic>draw</sic> thro the Center of<lb/>raight line in it, which<lb/>the Center, it shall cut it<lb/>it cuts at right angles<lb/>it</p><p><head>Prop VIII Theor</head>thout a Circle and straight lines be drawn from it to the circumference, whereof one<lb/>those which fall upon the concave circumference the greatest is that which passes<lb/>the rest, that which is nearer to that thro' the center is always greater than the<lb/>those which fall upon the convex circumference, the least is that between the<lb/>le and the diameter: and of the rest that which is nearer to the least is always<lb/>emote, and only two equal straight lines can be drawn from the point unto<lb/>one upon each side of the least.</p><p><head>Theor</head>ach other externally, the straight<lb/>ters shall pass thro' the point of</p><p><head>Prob</head>line from a given point, either<lb/>Circumference, which shall<lb/>cle.</p><p><head>Theor</head>of any quadrilateral fig-<lb/>circle, are together equal to</p><p><head>VII Theor.</head>the angles which stand upon<lb/>are equal to one another<lb/>the centers or circumfe-</p><pb/><head>Prop IV Theor</head>If in a Circle two straight lines cut one another,<lb/>which do not both pass thro' the Center, they do<lb/>not bisect each the other.<p><head>Prop XIII Theor</head>One circle cannot touch another in more points<lb/>than one, whether it touches it on the inside or<lb/>outside.</p><p><head>Prop XVIII Theor.</head>If a straight line touches a circle, the straight<lb/>line drawn from the Center to the point of Contact,<lb/>shall be perpendicular to the line touching the<lb/>circle.</p><p><head>Prop XXIII Theor.</head>Upon the same straight line & upon the same<lb/>side of it, there cannot be two similar segments<lb/>of circles, not coinciding with one another</p><p><head>Prop XXVII Theor</head>In equal circles equal straight lines cut off equal<lb/>circumferences, the greater equal to the greater<lb/>and the less to the less.</p><pb/> | ||
Books of Euclid as expressed by Simson. --
Theor.be draw thro the Center of
raight line in it, which
the Center, it shall cut it
it cuts at right angles
it
Prop VIII Theorthout a Circle and straight lines be drawn from it to the circumference, whereof one
those which fall upon the concave circumference the greatest is that which passes
the rest, that which is nearer to that thro' the center is always greater than the
those which fall upon the convex circumference, the least is that between the
le and the diameter: and of the rest that which is nearer to the least is always
emote, and only two equal straight lines can be drawn from the point unto
one upon each side of the least.
Theorach other externally, the straight
ters shall pass thro' the point of
Probline from a given point, either
Circumference, which shall
cle.
Theorof any quadrilateral fig-
circle, are together equal to
VII Theor.the angles which stand upon
are equal to one another
the centers or circumfe-
---page break---
Prop IV TheorIf in a Circle two straight lines cut one another,
which do not both pass thro' the Center, they do
not bisect each the other.
Prop XIII TheorOne circle cannot touch another in more points
than one, whether it touches it on the inside or
outside.
Prop XVIII Theor.If a straight line touches a circle, the straight
line drawn from the Center to the point of Contact,
shall be perpendicular to the line touching the
circle.
Prop XXIII Theor.Upon the same straight line & upon the same
side of it, there cannot be two similar segments
of circles, not coinciding with one another
Prop XXVII TheorIn equal circles equal straight lines cut off equal
circumferences, the greater equal to the greater
and the less to the less.
---page break---
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the propositions of the third and fourth books of euclid as expressed by simson |
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sir samuel bentham |
[[watermarks::[tall thin motif with prince of wales feathers] icv]] |
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