The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 10
... 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 coin- cide with the base EF , two straight lines would 10 Ax . inclose a space , which is impossible . * Therefore ...
... 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 coin- cide with the base EF , two straight lines would 10 Ax . inclose a space , which is impossible . * Therefore ...
Page 12
... base BC is common to the two triangles BFC , CGB ; wherefore these 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 ...
... base BC is common to the two triangles BFC , CGB ; wherefore these 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 ...
Page 13
... BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle + ACB ; therefore the + IIyp . base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater ...
... BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the angle + ACB ; therefore the + IIyp . base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater ...
Page 14
... base CD are equal to one another : but the 19 Ax . angle ECD is greater than the angle BCD : wherefore the angle FDC ... BC equal to the base EF . The angle BAC shall be equal to the angle EDF . For , if the trian- CE gle ABC be applied ...
... base CD are equal to one another : but the 19 Ax . angle ECD is greater than the angle BCD : wherefore the angle FDC ... BC equal to the base EF . The angle BAC shall be equal to the angle EDF . For , if the trian- CE gle ABC be applied ...
Page 15
... BC upon EF ; the point C shall also coincide with the point F , because BC is equal † to EF . + Hyp . Therefore BC coinciding with EF , BA and AC shall coincide with ED and DF : for , if the base BC coincides with the base EF , but the ...
... BC upon EF ; the point C shall also coincide with the point F , because BC is equal † to EF . + Hyp . Therefore BC coinciding with EF , BA and AC shall coincide with ED and DF : for , if the base BC coincides with the base EF , but the ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole