A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Page 15
... which has three equal sides . 25. An isosceles triangle is that which has only two sides equal . 26. A scalene triangle is that which has three unequal sides . 27. A right - angled triangle is that which has DEFINITIONS . 15.
... which has three equal sides . 25. An isosceles triangle is that which has only two sides equal . 26. A scalene triangle is that which has three unequal sides . 27. A right - angled triangle is that which has DEFINITIONS . 15.
Page 18
... unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same are equal to one another . 7. Things which are halves of the same are equal to one another . 8. Magnitudes which coincide ...
... unequal . 5. If equals be taken from unequals the remainders are unequal . 6. Things which are double of the same are equal to one another . 7. Things which are halves of the same are equal to one another . 8. Magnitudes which coincide ...
Page 26
... unequal to AC , that is , it is equal to it . Therefore , if two angles , & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . If the hypothesis and predicate of a proposition be made to change places , the ...
... unequal to AC , that is , it is equal to it . Therefore , if two angles , & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . If the hypothesis and predicate of a proposition be made to change places , the ...
Page 40
... unequal ; greater angle opposite to it . made between the 6th and 19th . Ex . Prove this proposition by producing the less side AB to E , making AE equal to AC , and joining CE . triangle are unequal , the angles and the greater side ...
... unequal ; greater angle opposite to it . made between the 6th and 19th . Ex . Prove this proposition by producing the less side AB to E , making AE equal to AC , and joining CE . triangle are unequal , the angles and the greater side ...
Page 50
... unequal to DE , that is , it is equal to it ; and BC is equal to EF ; [ Hyp . ] therefore the two sides AB , BC are equal to the two sides DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; [ Hyp . ] therefore the ...
... unequal to DE , that is , it is equal to it ; and BC is equal to EF ; [ Hyp . ] therefore the two sides AB , BC are equal to the two sides DE , EF , each to each ; and the angle ABC is equal to the angle DEF ; [ Hyp . ] therefore the ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides No preview available - 2015 |
Common terms and phrases
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle DBA angle EDF angle equal angles are equal axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid EUCLID'S ELEMENTS 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 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
Popular passages
Page 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.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 41 - Any two sides of a triangle are together greater than the third side.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.