Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 24
... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the ... angle FAG common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and ...
... remaining angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the ... angle FAG common to the two trian- gles , AFC , AGB ; therefore the base FC is equal ( 4. 1. ) to the base GB , and ...
Σελίδα 25
... angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles are equal , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the ...
... angle BFC is equal to the angle CGB ; wherefore the triangles BFC , CGB are equal ( 3. 1. ) , and their remaining angles are equal , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the ...
Σελίδα 30
... angle ABC ; then will the two angles DBA , ABC be equal to the three angles DBE , EBA , ABC ; but the angles CBE ... angle ABC , and the remain . ing angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater ...
... angle ABC ; then will the two angles DBA , ABC be equal to the three angles DBE , EBA , ABC ; but the angles CBE ... angle ABC , and the remain . ing angle ABE is equal ( 3. Ax . ) to the remaining angle ABD , the less to the greater ...
Σελίδα 31
... remaining angle CEA it A- -B E D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner may be ... angle is greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be ...
... remaining angle CEA it A- -B E D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner may be ... angle is greater than either of the interior , and opposite angles . Let ABC be a triangle , and let its side BC be ...
Σελίδα 39
... angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . If a straight ...
... angle BGH ; therefore the remaining angle AGH is equal to the remaining angle GHD ; and they are alternate angles ; there- fore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXIX . THEOR . If a straight ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore