The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 σελίδες |
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Σελίδα 7
... Wherefore CA , AB , BC , are equal to one another ; and therefore 4. The triangle ABC is equilateral ; and it is described upon the given straight line AB . Which was to be done . PROP . II . - PROBLEM . From a given point to draw a ...
... Wherefore CA , AB , BC , are equal to one another ; and therefore 4. The triangle ABC is equilateral ; and it is described upon the given straight line AB . Which was to be done . PROP . II . - PROBLEM . From a given point to draw a ...
Σελίδα 8
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4. The straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore 4. The straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn ...
Σελίδα 9
... wherefore also 3. The point C shall coincide with the point F , because the straight line AC is equal to DF . But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ; because , the point B ...
... wherefore also 3. The point C shall coincide with the point F , because the straight line AC is equal to DF . But the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF ; because , the point B ...
Σελίδα 10
... wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their remaining angles are equal , each to each , to which the equal sides are opposite ; therefore 5. The angle FBC is equal to the angle GCB , and the angle BCF to the ...
... wherefore ( I. 4. ) 4. The triangles BFC , CGB , are equal , and their remaining angles are equal , each to each , to which the equal sides are opposite ; therefore 5. The angle FBC is equal to the angle GCB , and the angle BCF to the ...
Σελίδα 11
... Wherefore , if two angles , & c . Q.E.D. COR . - Hence every equiangular triangle is also equilateral . PROP . VII . - THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ...
... Wherefore , if two angles , & c . Q.E.D. COR . - Hence every equiangular triangle is also equilateral . PROP . VII . - THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which ...
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AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle