A Text-book of Euclid's Elements for the Use of Schools, Libro 1Macmillan, 1904 - 456 páginas |
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Página 36
... a rhombus ; and the diagonal AC is bisected at O. If O is joined to the angular points B and D ; shew that OB and OD are in one straight line . PROPOSITION 15. THEOREM . If two straight lines intersect one 36 EUCLID'S ELEMENTS .
... a rhombus ; and the diagonal AC is bisected at O. If O is joined to the angular points B and D ; shew that OB and OD are in one straight line . PROPOSITION 15. THEOREM . If two straight lines intersect one 36 EUCLID'S ELEMENTS .
Página 37
Euclid. PROPOSITION 15. THEOREM . If two straight lines intersect one another , then the vertically opposite angles shall be equal . B A Let the two straight lines AB , CD cut one another at the point E. Then ( i ) the angle AEC shall be ...
Euclid. PROPOSITION 15. THEOREM . If two straight lines intersect one another , then the vertically opposite angles shall be equal . B A Let the two straight lines AB , CD cut one another at the point E. Then ( i ) the angle AEC shall be ...
Página 55
... intersecting straight lines . In what case is this impossible ? 9. Through a given point draw a straight line such that the per- pendiculars drawn to it from two given points may be equal . In what case is this impossible ? SECTION II ...
... intersecting straight lines . In what case is this impossible ? 9. Through a given point draw a straight line such that the per- pendiculars drawn to it from two given points may be equal . In what case is this impossible ? SECTION II ...
Página 61
... intersecting straight lines cannot be both parallel to a third straight line . This statement is known as Playfair's Axiom ; and though it is not altogether free from objection , it is no doubt simpler and more fundamental than that ...
... intersecting straight lines cannot be both parallel to a third straight line . This statement is known as Playfair's Axiom ; and though it is not altogether free from objection , it is no doubt simpler and more fundamental than that ...
Página 62
... intersecting straight lines both parallel to a third straight line : which is impossible . Therefore AB and CD never meet ; that is , they are parallel . PROBLEM . PROPOSITION 31 . To draw a straight line 62 EUCLID'S ELEMENTS .
... intersecting straight lines both parallel to a third straight line : which is impossible . Therefore AB and CD never meet ; that is , they are parallel . PROBLEM . PROPOSITION 31 . To draw a straight line 62 EUCLID'S ELEMENTS .
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 326 - From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Página 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...
Página 291 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 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.
Página 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.
Página 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.