A Text-book of Euclid's Elements for the Use of Schools, Book 1 |
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Page 2
... difference of the angles AOC and BOC . [ Another view of an angle is recognized in many branches of mathematics ; and though not employed by Euclid , it is here given because it furnishes more clearly than any other a conception of what ...
... difference of the angles AOC and BOC . [ Another view of an angle is recognized in many branches of mathematics ; and though not employed by Euclid , it is here given because it furnishes more clearly than any other a conception of what ...
Page 44
... difference of any two sides of a triangle is less than the third side . 8. In a quadrilateral , if two opposite sides which are not parallel are produced to meet one another ; shew that the perimeter of the greater of the two triangles ...
... difference of any two sides of a triangle is less than the third side . 8. In a quadrilateral , if two opposite sides which are not parallel are produced to meet one another ; shew that the perimeter of the greater of the two triangles ...
Page 92
... difference of the squares on the sides AB and AC , is equal to the difference of the squares on BX and CX , the segments of the base . 8. If from any point O within a triangle ABC , perpendiculars OX , OY , OZ are drawn to the sides BC ...
... difference of the squares on the sides AB and AC , is equal to the difference of the squares on BX and CX , the segments of the base . 8. If from any point O within a triangle ABC , perpendiculars OX , OY , OZ are drawn to the sides BC ...
Page 103
... line parallel to the base BC , and meeting the other sides in D and E , so that DE may be equal to the difference of BD and CE . IV . ON PARALLELOGRAMS . See Propositions 33 , 34 THEOREMS AND EXAMPLES ON BOOK I. 103 ON PARALLELS.
... line parallel to the base BC , and meeting the other sides in D and E , so that DE may be equal to the difference of BD and CE . IV . ON PARALLELOGRAMS . See Propositions 33 , 34 THEOREMS AND EXAMPLES ON BOOK I. 103 ON PARALLELS.
Page 105
... difference of the parallel sides . DEFINITION . If from the extremities of one straight line perpendiculars are drawn to another , the portion of the latter intercepted between the perpendiculars is said to be the Orthogonal Projection ...
... difference of the parallel sides . DEFINITION . If from the extremities of one straight line perpendiculars are drawn to another , the portion of the latter intercepted between the perpendiculars is said to be the Orthogonal Projection ...
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Common terms and phrases
ABCD AC is equal adjacent angles Algebra angle BAC angle equal base BC bisected bisectors centre chord circumference circumscribed circle concyclic Constr Describe a circle diagonal diameter divided equal angles equiangular Euclid Euclid's exterior angle find the locus given circle given point given straight line given triangle greater Hence hypotenuse inscribed circle isosceles triangle Let ABC line which joins magnitudes meet middle point nine-points circle opposite sides orthocentre par¹ parallelogram parm pass pedal triangle perp perpendiculars drawn plane XY polygon produced Proof proportional PROPOSITION PROPOSITION 13 prove quadrilateral radical axis radius rectangle contained rectilineal figure regular polygon right angles segment shew shewn side BC Similarly square straight line drawn tangent THEOREM triangle ABC twice the rect vertex vertical angle
Popular passages
Page 353 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 340 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 65 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 162 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Page 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Page 162 - 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, together •with the square...
Page 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Page 79 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 18 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Page 242 - We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent ; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.