A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 22
... base BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , B and the other angles shall be equal each to each , to which the equal sides are opposite , namely , the angle ABC to the angle DEF , and the angle ACB ...
... base BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , B and the other angles shall be equal each to each , to which the equal sides are opposite , namely , the angle ABC to the angle DEF , and the angle ACB ...
Página 23
Euclides Charles MANSFORD. point E , therefore the base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which ...
Euclides Charles MANSFORD. point E , therefore the base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which ...
Página 25
... base . Therefore the angles , & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . If the ... BC is common to both , the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the BOOK I. 6 . 25.
... base . Therefore the angles , & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . If the ... BC is common to both , the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the BOOK I. 6 . 25.
Página 27
... base , equal to one another , and likewise their sides CB , DB , that are terminated in B. A CD B 2 . 3 . Join CD ... BC is equal to BD [ Hyp . ] , the angle BDC is equal to the angle BCD . [ I. 5. ] But it has been proved to be greater ...
... base , equal to one another , and likewise their sides CB , DB , that are terminated in B. A CD B 2 . 3 . Join CD ... BC is equal to BD [ Hyp . ] , the angle BDC is equal to the angle BCD . [ I. 5. ] But it has been proved to be greater ...
Página 28
... base & c . Q.E.D. This proposition is introduced for the sole purpose of leading on to prop . 8 , and as this latter can be proved by other and easier methods , prop . 7 might ... base BC coincides with the base EF 28 EUCLID'S ELEMENTS .
... base & c . Q.E.D. This proposition is introduced for the sole purpose of leading on to prop . 8 , and as this latter can be proved by other and easier methods , prop . 7 might ... base BC coincides with the base EF 28 EUCLID'S ELEMENTS .
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CBA axioms base BC BC is equal bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop PROPOSITION quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal