A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
Dentro del libro
Página 6
If a leaf of paper be folded and divided into two equal parts by creasing it down the middle , the crease will represent a straight line . Now such a crease does not belong to either half of the paper , but simply divides one half from ...
If a leaf of paper be folded and divided into two equal parts by creasing it down the middle , the crease will represent a straight line . Now such a crease does not belong to either half of the paper , but simply divides one half from ...
Página 10
Then follows the discussion , which may be divided into three parts to be thus distinguished . 1. The particular enunciation . The construction . 3. The demonstration . The demonstration is effected by combining the elementary truths ...
Then follows the discussion , which may be divided into three parts to be thus distinguished . 1. The particular enunciation . The construction . 3. The demonstration . The demonstration is effected by combining the elementary truths ...
Página 23
Prove by the method used in this proposition that the two triangles into which a square is divided by its diagonal are equal to one another . 2. The diagonals of a square are equal to one another . PROPOSITION 5. THEOREM .
Prove by the method used in this proposition that the two triangles into which a square is divided by its diagonal are equal to one another . 2. The diagonals of a square are equal to one another . PROPOSITION 5. THEOREM .
Página 31
Therefore the straight line AB is divided into two equal parts at the point D. Q.E.F. Ex . The straight line which bisects the vertical angle of an isosceles triangle also bisects the base at right angles . 3 3 PROPOSITION 11. PROBLEM .
Therefore the straight line AB is divided into two equal parts at the point D. Q.E.F. Ex . The straight line which bisects the vertical angle of an isosceles triangle also bisects the base at right angles . 3 3 PROPOSITION 11. PROBLEM .
Página 59
N.B. — In the case of a regular figure , as all its angles are equal , the value of an exterior angle will be found by dividing four right angles by the number of sides of the figure ; and if the quotient ...
N.B. — In the case of a regular figure , as all its angles are equal , the value of an exterior angle will be found by dividing four right angles by the number of sides of the figure ; and if the quotient ...
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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 |