The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 6
... remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remain- ders are unequal . VI . Things which are double of the same , EUCLID'S ELEMENTS . AXIOMS. ...
... remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remain- ders are unequal . VI . Things which are double of the same , EUCLID'S ELEMENTS . AXIOMS. ...
Page 7
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Page 37
... double * of the tri- * 34 . 1 . angle BDC ; and they are therefore equal † to † 6 ax . one another . * But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then ...
... double * of the tri- * 34 . 1 . angle BDC ; and they are therefore equal † to † 6 ax . one another . * But , if the sides AD , EF , opposite to the base BC of the parallelograms ABCD , EBCF , be not terminated in the same point ; then ...
Page 41
... double of the triangle ABC , because the diameter AC divides it into two equal * * 34 . 1 . parts ; wherefore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB . To describe a ...
... double of the triangle ABC , because the diameter AC divides it into two equal * * 34 . 1 . parts ; wherefore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB . To describe a ...
Page 42
... double of the triangle AEC : but * 41 . 1. the parallelogram FECG is likewise double * of the triangle AEC , because they are upon the same base EC , and between the same parallels EC , AG : therefore the parallelogram FECG is +6 Ax ...
... double of the triangle AEC : but * 41 . 1. the parallelogram FECG is likewise double * of the triangle AEC , because they are upon the same base EC , and between the same parallels EC , AG : therefore the parallelogram FECG is +6 Ax ...
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