Elementary Geometry, Τόμος 2 |
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Σελίδα vii
... joins the centres of two intersecting circles , or that line produced , bisects at right angles their common chord THEOREM II . If two circles touch one another , the line that joins their centres will pass through the point of contact ...
... joins the centres of two intersecting circles , or that line produced , bisects at right angles their common chord THEOREM II . If two circles touch one another , the line that joins their centres will pass through the point of contact ...
Σελίδα 1
... called a sector . Def . 7. The line joining the extremities of an arc is called a chord of that arc . Def . 8. The parts into which a chord divides a circle are called segments . B Several properties of a circle follow at once from the.
... called a sector . Def . 7. The line joining the extremities of an arc is called a chord of that arc . Def . 8. The parts into which a chord divides a circle are called segments . B Several properties of a circle follow at once from the.
Σελίδα 8
... Join AB , BC . Then since AB is to be a chord , the locus of the centre is the straight line that bisects AB at right angles . ( Th . 2 , Cor . B. ) Similarly , the line that bisects BC at right angles must pass through the centre ...
... Join AB , BC . Then since AB is to be a chord , the locus of the centre is the straight line that bisects AB at right angles . ( Th . 2 , Cor . B. ) Similarly , the line that bisects BC at right angles must pass through the centre ...
Σελίδα 9
... Join OC , OA . Then since M and N are right angles , therefore and but therefore D OM2 + MC2 = OC3 , ON2 + NA = OA , M N OCOA , and OC2 = OA2 ; OM2 + MC2 = ON2 + NAo . Hence , ( 1 ) if AB = CD and AN = CM , it follows that OM = ON . ( 2 ) ...
... Join OC , OA . Then since M and N are right angles , therefore and but therefore D OM2 + MC2 = OC3 , ON2 + NA = OA , M N OCOA , and OC2 = OA2 ; OM2 + MC2 = ON2 + NAo . Hence , ( 1 ) if AB = CD and AN = CM , it follows that OM = ON . ( 2 ) ...
Σελίδα 11
... Join PO , and produce it to Q. Then because , from the definition of a circle , OPA is an isosceles triangle , the angle OAP = the angle OPA : but the exterior angle AOQ is equal to the two interior and opposite angles OAP and OPA , and ...
... Join PO , and produce it to Q. Then because , from the definition of a circle , OPA is an isosceles triangle , the angle OAP = the angle OPA : but the exterior angle AOQ is equal to the two interior and opposite angles OAP and OPA , and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD Algebra angle AOB angular points ARITHMETIC base bisectors bisects the angle BROOKE FOSS WESTCOTT Cambridge centre circles touch circumference circumscribed cloth common measure common tangents Construction Crown 8vo decagon Describe a circle diameter divided drawn EDUCATIONAL BOOKS ELEMENTARY TREATISE equal arcs equal chords equiangular equilateral triangle Examples Fcap find the locus follows GEOMETRY given circle given line given point given ratio given straight line Hence homologous hypothenuse incommensurable inscribed intersect John's College Join Let ABC LIST OF EDUCATIONAL magnitudes Mathematical mean proportional middle points numerical values parallel parallelograms pass perimeter perpendicular point of contact PROBLEM prove Ptolemy's Theorem quadrilateral figure radii radius rectangle contained regular polygon right angles Schools secant Second Edition segments shew shewn similar triangles SPQR student subtend equal angles tangent THEOREM triangle ABC vertical angle
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