A School Geometry, Deler 1-4Macmillan and Company, 1908 |
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Side xiii
... segment in each being towards the angular point . Areas . PART II . 97 16 99 DEFINITIONS THEOREM 23. AREA OF A RECTANGLE . 100 THEOREM 24. [ Euc . I. 35. ] Parallelograms on the same base and between the same parallels are equal in area ...
... segment in each being towards the angular point . Areas . PART II . 97 16 99 DEFINITIONS THEOREM 23. AREA OF A RECTANGLE . 100 THEOREM 24. [ Euc . I. 35. ] Parallelograms on the same base and between the same parallels are equal in area ...
Side xv
... segment of a circle are equal . CONVERSE OF THEOREM 39. Equal angles standing on the same base , and on the same ... segment greater than a semi - circle is acute ; and the angle in a segment less than a semi - circle is obtuse . 165 ...
... segment of a circle are equal . CONVERSE OF THEOREM 39. Equal angles standing on the same base , and on the same ... segment greater than a semi - circle is acute ; and the angle in a segment less than a semi - circle is obtuse . 165 ...
Side xvi
... segments of the circle . 178 180 Problems . GEOMETRICAL ANALYSIS 182 PROBLEM 20. Given a circle , or an arc of a circle , to find its centre . 183 PROBLEM 21. To bisect a given arc . 183 PROBLEM 22 . · To draw a tangent to a xvi CONTENTS .
... segments of the circle . 178 180 Problems . GEOMETRICAL ANALYSIS 182 PROBLEM 20. Given a circle , or an arc of a circle , to find its centre . 183 PROBLEM 21. To bisect a given arc . 183 PROBLEM 22 . · To draw a tangent to a xvi CONTENTS .
Side xvii
... segment of a circle which shall contain an angle equal to a given angle . COR . To cut off from a given circle a segment containing a given angle , it is enough to draw a tangent to the circle , and from the point of contact to draw a ...
... segment of a circle which shall contain an angle equal to a given angle . COR . To cut off from a given circle a segment containing a given angle , it is enough to draw a tangent to the circle , and from the point of contact to draw a ...
Side xviii
... segments together with twice the rectangle contained by the segments . THEOREM 52. [ Euc . II . 7. ] If a straight line is divided externally at any point , the square on the given line is equal to the sum of the squares on the two ...
... segments together with twice the rectangle contained by the segments . THEOREM 52. [ Euc . II . 7. ] If a straight line is divided externally at any point , the square on the given line is equal to the sum of the squares on the two ...
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Vanlige uttrykk og setninger
AB² adjacent angles altitude angle equal base BC bisector bisects circle of radius circle whose centre circles which touch circum-circle circumference circumscribed coincide common tangents concyclic Construct a triangle diagonals diagram diameter distance divided draw a circle equal in area equidistant escribed circles Euclid exterior angles Find the area find the locus given angle given circle given point given straight line given triangle greater Hence hypotenuse inches inscribed isosceles triangle length Let ABC meet metres middle point millimetre nine-points circle opposite sides orthocentre par¹ parallelogram pedal triangle perp PROBLEM produced Proof radii rect rectangle rectangle contained rectilineal figure required to prove respectively rhombus right angles right-angled triangle segment shew shewn straight line drawn tangent Theor Theorem trapezium triangle ABC triangles are equal vertex vertical angle
Populære avsnitt
Side xi - IF two triangles have two angles of one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...
Side 44 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 190 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Side 12 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 122 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side x - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 65 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.