The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II.): Books III.-VIW.S. Sonnenschein, 1888 |
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Σελίδα 51
... point . The point is called the point of contact . THEOR . 20. Aliter . Let A be a point on the circumference of the circle ABC whose centre is O , GAH a straight line through A not perpen- dicular to OA : then shall GH meet the ...
... point . The point is called the point of contact . THEOR . 20. Aliter . Let A be a point on the circumference of the circle ABC whose centre is O , GAH a straight line through A not perpen- dicular to OA : then shall GH meet the ...
Σελίδα 52
... point L. Next , let the point L move along the circumference of the circle ... points of intersection continually approach , and ultimately coincide with one ... contact . Theor . 20 may be restated as in the first 52 THE ELEMENTS OF ...
... point L. Next , let the point L move along the circumference of the circle ... points of intersection continually approach , and ultimately coincide with one ... contact . Theor . 20 may be restated as in the first 52 THE ELEMENTS OF ...
Σελίδα 53
... point of contact . COR . 3. The centre of a circle lies in the perpendicular to any tangent at the point of contact . For only one perpendicular can be drawn to a tangent from the point of contact . COR . 4. The straight line drawn from ...
... point of contact . COR . 3. The centre of a circle lies in the perpendicular to any tangent at the point of contact . For only one perpendicular can be drawn to a tangent from the point of contact . COR . 4. The straight line drawn from ...
Σελίδα 57
... point . THEOR . 23. The adjacent angles contained by a tangent and a chord drawn from the point of contact are equal to the angles in the segments into which the chord divides the circle , each to the angle in the segment alternate to ...
... point . THEOR . 23. The adjacent angles contained by a tangent and a chord drawn from the point of contact are equal to the angles in the segments into which the chord divides the circle , each to the angle in the segment alternate to ...
Σελίδα 62
... point A on the circumference of the circle draw the tangent AE , and draw the chord AB , making with AE an angle ... point of contact , therefore the angle BAE is equal to the angle in the segment ACB , alternate to BAE . III . 23 . But ...
... point A on the circumference of the circle draw the tangent AE , and draw the chord AB , making with AE an angle ... point of contact , therefore the angle BAE is equal to the angle in the segment ACB , alternate to BAE . III . 23 . But ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle BAC angle DAE angle DEF angle HBK angular points antecedent base chord HK circle ABC circle whose centre circles touch circumscribed circle decagon diagonal diameter divided internally draw duplicate ratio equal angles equiangular equimultiples externally given circle given point given ratio given straight line greater half the angle Hence homologous sides inscribed circle isosceles triangle less Let ABC line joining mean proportional meet the circumference middle point minor arc HK multiple nine-points circle orthocentre parallel parallelogram perpendicular PLANE GEOMETRY point of contact polygon Prob Prove Q.E.D. THEOR quadrilateral radii radius ratio compounded ratios are equal rectangle BD rectangle contained rectilineal figure right angles sector segment BAC semicircle Shew side BC square straight line drawn tangent triangle ABC triangle DEF vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 167 - 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.
Σελίδα 9 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
Σελίδα 30 - In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Σελίδα 171 - ... are to one another in the duplicate ratio of their homologous sides.
Σελίδα 150 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Σελίδα 115 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let...
Σελίδα 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 96 - ... if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Σελίδα 150 - When there are any number of magnitudes of the same kind, the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second, and of the ratio whi.ch the second has to the third, and of the ratio which the third has to the fourth, and so on unto the last magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first...