The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 17
... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible . Therefore a 10. Ax . the ...
... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does not coincide with the base EF , two straight lines would inclose a space , which is impossible . Therefore a 10. Ax . the ...
Página 18
... base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle ...
... base BC is common to the two triangles BFC , CGB ; wherefore the triangles are equal , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle FBC is equal to the angle GCB , and the angle ...
Página 19
... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ...
... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; therefore the base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB ...
Página 20
... base CD are equal to one another , but the angle ECD is greater than the ... base , and on the same side of it , there cannot be two triangles that have their sides which ... BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
... base CD are equal to one another , but the angle ECD is greater than the ... base , and on the same side of it , there cannot be two triangles that have their sides which ... BC is equal to EF ; therefore BC coinciding with 20 THE ELEMENTS.
Página 21
Euclid Robert Simson. BC is equal to EF ; therefore BC coinciding with EF , BA and Book I AC shall coincide with ED and DF ; for , if the base BC coin- cides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD ...
Euclid Robert Simson. BC is equal to EF ; therefore BC coinciding with EF , BA and Book I AC shall coincide with ED and DF ; for , if the base BC coin- cides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore