A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 28
... triangle is a rigid figure ; i.e. , its sides cannot be forced into any ... ABC , DEF be two triangles , having the two sides AB , AC equal to the two ... triangle ABC be applied to the 2 , 3 . triangle DEF , so that the point B may be on ...
... triangle is a rigid figure ; i.e. , its sides cannot be forced into any ... ABC , DEF be two triangles , having the two sides AB , AC equal to the two ... triangle ABC be applied to the 2 , 3 . triangle DEF , so that the point B may be on ...
Página 29
... triangles equal in this prop . When triangles are to be proved equal , he always appeals to prop . 4. The demonstration of this prop . may be conducted thus : For let the triangle DEF be applied to ABC so that the bases may coincide ...
... triangles equal in this prop . When triangles are to be proved equal , he always appeals to prop . 4. The demonstration of this prop . may be conducted thus : For let the triangle DEF be applied to ABC so that the bases may coincide ...
Página 31
... triangle ABC [ I. 1 ] , and bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. Because AC is equal to CB [ Def . 24 ] , and CD 3. is common to the two triangles ACD , BCD ...
... triangle ABC [ I. 1 ] , and bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. Because AC is equal to CB [ Def . 24 ] , and CD 3. is common to the two triangles ACD , BCD ...
Página 38
Euclides Charles MANSFORD. PROPOSITION 16. THEOREM . If one side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let one side BC be 1 . produced to ...
Euclides Charles MANSFORD. PROPOSITION 16. THEOREM . If one side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let one side BC be 1 . produced to ...
Página 39
... ABC be any triangle : any two of its angles are together less than two right angles . Produce BC to 2. D. 3 . Then because ACD is the ex- terior angle of the tri- angle ABC , it is greater than the interior and opposite angle ABC . B ...
... ABC be any triangle : any two of its angles are together less than two right angles . Produce BC to 2. D. 3 . Then because ACD is the ex- terior angle of the tri- angle ABC , it is greater than the interior and opposite angle ABC . B ...
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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
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw drawn equal sides equal to AC equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure remainder result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole
Pasajes populares
Página 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Página 28 - If two triangles have two sides of the one equal to two sides of the...
Página 41 - Any two sides of a triangle are together greater than the third side.
Página 57 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Página 72 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Página 75 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Página 55 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Página 28 - A two triangles, having the two sides AB, AC, equal to the two sides \ DE, DF, each to each, viz: AB to DE, and AC to DF; and also the base BC equal to the base EF.
Página 69 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.