A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
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Página 51
angle ABH is equal to the angle DEF [ Hyp . ] ; therefore the base AH is equal to the base DF , and the triangle ABH to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ...
angle ABH is equal to the angle DEF [ Hyp . ] ; therefore the base AH is equal to the base DF , and the triangle ABH to the triangle DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ...
Página 52
And it should be noticed that there is this difference between them : the angle ACB opposite AB in the one triangle is ... will not be equal unless the angle opposite the other pair of equal sides is of the same species in each triangle ...
And it should be noticed that there is this difference between them : the angle ACB opposite AB in the one triangle is ... will not be equal unless the angle opposite the other pair of equal sides is of the same species in each triangle ...
Página 61
Then because AB is parallel to CD ( Hyp . ] and 3 . ... The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . Let ACBD be a parallelogram ...
Then because AB is parallel to CD ( Hyp . ] and 3 . ... The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . Let ACBD be a parallelogram ...
Página 62
A D to one another . [ I. 29. ] And because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD are equal to one another . [ I. 29. ] ... PROPOSITION 35. THEOREM . Parallelograms on the same base , 62 EUCLID'S ELEMENTS .
A D to one another . [ I. 29. ] And because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD are equal to one another . [ I. 29. ] ... PROPOSITION 35. THEOREM . Parallelograms on the same base , 62 EUCLID'S ELEMENTS .
Página 64
At this point we enter upon the “ third section ” of the First Book , which treats of triangles and parallelograms upon equal bases , and between the same parallels and their relation to one another . Ex . 1.
At this point we enter upon the “ third section ” of the First Book , which treats of triangles and parallelograms upon equal bases , and between the same parallels and their relation to one another . Ex . 1.
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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
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angle equal apply 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 half Hence isosceles triangle join length less Let ABC meet method middle points namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained remainder result right angles shew 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.
Información bibliográfica
| Título | A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
| Autor | Euclides |
| Editor | Charles MANSFORD |
| Publicado | 1874 |
| Procedencia del original | Universidad de Oxford |
| Digitalizado | 7 Sep. 2006 |
| Exportar cita | BiBTeX EndNote RefMan |