A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Page 14
... perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . 13. A term or boundary is the extremity of any thing . 14 . A figure is that which is ...
... perpendicular to it . 11. An obtuse angle is that which is greater than a right angle . 12. An acute angle is that which is less than a right angle . 13. A term or boundary is the extremity of any thing . 14 . A figure is that which is ...
Page 32
... perpendicular to a given straight line of unlimited length , from a given point without it . 1 . Let AB be the given straight line , which may be produced to any length both ways , and let C be a given point without it . It is required ...
... perpendicular to a given straight line of unlimited length , from a given point without it . 1 . Let AB be the given straight line , which may be produced to any length both ways , and let C be a given point without it . It is required ...
Page 33
... perpendicular to it . [ Def . 10. ] Therefore a perpendicular CH has been drawn to the given straight line AB from the given point C without it . Q.E.F. The given line must be of unlimited length to insure that the circle FDE will meet ...
... perpendicular to it . [ Def . 10. ] Therefore a perpendicular CH has been drawn to the given straight line AB from the given point C without it . Q.E.F. The given line must be of unlimited length to insure that the circle FDE will meet ...
Page 34
... perpendicular to AB . Join EG and DG . The proof is identical with exercise 2 to prop . 9 . Ex . From a given point to draw a straight line equally inclined to two given straight lines which cut one another . [ See Ex . to last two ...
... perpendicular to AB . Join EG and DG . The proof is identical with exercise 2 to prop . 9 . Ex . From a given point to draw a straight line equally inclined to two given straight lines which cut one another . [ See Ex . to last two ...
Page 39
... perpendicular can be drawn from the same point to the same straight line . 3. The equal angles of an isosceles triangle must be both acute . PROPOSITION 18 . THEOREM . The greater side of every triangle is opposite to the greater angle ...
... perpendicular can be drawn from the same point to the same straight line . 3. The equal angles of an isosceles triangle must be both acute . PROPOSITION 18 . THEOREM . The greater side of every triangle is opposite to the greater angle ...
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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.