A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 10
... most con- vincing way . Such a syllogism generally takes the following form , which may therefore be regarded as the pattern of all geometrical reasoning . 1. All right angles are equal to one another . X INTRODUCTION .
... most con- vincing way . Such a syllogism generally takes the following form , which may therefore be regarded as the pattern of all geometrical reasoning . 1. All right angles are equal to one another . X INTRODUCTION .
Página 23
... 1 . side AB equal to the side AC , and let the straight lines AB , AC be produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . 2 . In BD take any point F , and BOOK I. 5 . 23.
... 1 . side AB equal to the side AC , and let the straight lines AB , AC be produced to D and E ; the angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . 2 . In BD take any point F , and BOOK I. 5 . 23.
Página 24
Euclides Charles MANSFORD. 2 . In BD take any point F , and from AE the greater cut off AG equal to AF the less , [ I.3 . ] and join FC , GB . 3 . Because A Fis equal to AG , [ Con . ] and AB to AC , [ Hyp . ] the two sides FA , AC are ...
Euclides Charles MANSFORD. 2 . In BD take any point F , and from AE the greater cut off AG equal to AF the less , [ I.3 . ] and join FC , GB . 3 . Because A Fis equal to AG , [ Con . ] and AB to AC , [ Hyp . ] the two sides FA , AC are ...
Página 25
... Take Fin AB , and making AG equal to AF , show that the angles ABC and ACB are equal to one another . 2. The opposite angles of a rhombus are equal to one another . [ Draw the diagonal . ] PROPOSITION 6. THEOREM . If two angles of a ...
... Take Fin AB , and making AG equal to AF , show that the angles ABC and ACB are equal to one another . 2. The opposite angles of a rhombus are equal to one another . [ Draw the diagonal . ] PROPOSITION 6. THEOREM . If two angles of a ...
Página 30
... Take any point D in AB , and 2. from AC cut off AE equal to AD [ I. 3 ] ; join DE , and on DE on the side remote from A describe the equilateral triangle DEF . [ I. 1. ] Join AF . The straight line AF shall bi- sect the angle BAC . 3 ...
... Take any point D in AB , and 2. from AC cut off AE equal to AD [ I. 3 ] ; join DE , and on DE on the side remote from A describe the equilateral triangle DEF . [ I. 1. ] Join AF . The straight line AF shall bi- sect the angle BAC . 3 ...
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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.