. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. qual to C, the less. a From the point A draw ^ the straight line AD equal to C ; andfrom the centre A, and at the dis- b 3. Post, tance AD, describe ^ the circle DEF ; and because A is the cen- F tre of the circle DEF, AE shall be equal to AD ; but the straightline C is likewise equal to AD ; whence
. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. qual to C, the less. a From the point A draw ^ the straight line AD equal to C ; andfrom the centre A, and at the dis- b 3. Post, tance AD, describe ^ the circle DEF ; and because A is the cen- F tre of the circle DEF, AE shall be equal to AD ; but the straightline C is likewise equal to AD ; whence AE and C are each ofthem equal to AD: wherefore the straight line AE is equal to*^C, and from AB, the greater of two straight lines, a part AE hasbeen cut off equal to C the less. Which was to he done. PROP. IV. THEOREM. IF two triangles have two sides of the one equalto two sides of the other, each to each; and havelikewise the angles contained by those sides equalto one another; they shall likewise have their bases,or third sides, equal; and the two triangles shall beequal; and their other angles shall be equal, each toeach, viz. those to which the equal sides are opposite. Let ABC, DEF be two triangles which have the two sidesAB, AC equal to the two sides DE, DF, each to each, c 1. Ax.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
