Elements of Plane GeometryE.H. Butler & Company, 1882 - 196 σελίδες |
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Σελίδα 86
... radii drawn to its extremities ; as , OFM . 177. A Tangent is a straight line Α which touches the circumference but ... radii are equal ; also , all its M N 0 diameters are equal . It also follows from the definition that circles are ...
... radii drawn to its extremities ; as , OFM . 177. A Tangent is a straight line Α which touches the circumference but ... radii are equal ; also , all its M N 0 diameters are equal . It also follows from the definition that circles are ...
Σελίδα 87
Franklin Ibach. CHORDS , ARCS , ANGLES AT THE CENTRE , SECANTS , AND RADII . THEOREM I. 183. Any diameter bisects the circle and its circumference . Let ABCD be a O , and AB any diameter . C A B D To prove that ABC — ABD . = On AB as an ...
Franklin Ibach. CHORDS , ARCS , ANGLES AT THE CENTRE , SECANTS , AND RADII . THEOREM I. 183. Any diameter bisects the circle and its circumference . Let ABCD be a O , and AB any diameter . C A B D To prove that ABC — ABD . = On AB as an ...
Σελίδα 89
... radii OA , OB , OD , ОА = OB = OD . ( 182 ) If AB could cut the circumference at A , B , and D , there would be three equal straight lines drawn from the same point to the same straight line , which cannot be . ( 61 ) ... a straight ...
... radii OA , OB , OD , ОА = OB = OD . ( 182 ) If AB could cut the circumference at A , B , and D , there would be three equal straight lines drawn from the same point to the same straight line , which cannot be . ( 61 ) ... a straight ...
Σελίδα 91
... radii OA , OB , PC , PD . F ОА PC , ( 182 ) OB = PD , ( 182 ) and La = Lb ; ( 187 ) A ABOA CDP , ( 83 ) and chord AB chord CD . Q. E. D. 189. COR . - In equal circles , or in the same circle , equal chords subtend equal arcs . THEOREM ...
... radii OA , OB , PC , PD . F ОА PC , ( 182 ) OB = PD , ( 182 ) and La = Lb ; ( 187 ) A ABOA CDP , ( 83 ) and chord AB chord CD . Q. E. D. 189. COR . - In equal circles , or in the same circle , equal chords subtend equal arcs . THEOREM ...
Σελίδα 92
... radii OA and OB . OA = OB , ( 182 ) and OD = OD ; RA AODRA BOD , ( 91 ) AD = = BD . and Also La = Lb ; arc AC- = arc BC . ( 186 ) Q. E. D. 191. COR . - The perpendicular erected at the middle point of a chord passes through the centre ...
... radii OA and OB . OA = OB , ( 182 ) and OD = OD ; RA AODRA BOD , ( 91 ) AD = = BD . and Also La = Lb ; arc AC- = arc BC . ( 186 ) Q. E. D. 191. COR . - The perpendicular erected at the middle point of a chord passes through the centre ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABC and DEF AC and BC acute angle adjacent angles angles are equal angles equals angles formed arc AC BC² bisectors bisects centre CF meet chord common point Concave Polygon construct Convex Polygon COR.-The decagon DEF are similar diagonal BC diameter Draw the diagonal equally distant equals two right equiangular Equilateral Polygon exterior angles given circle given straight line homologous sides hypothenuse included angle intersect La=Lb Let ABCD line joining lines drawn measured by arc medial lines middle point oblique lines parallelogram perimeter PLANE GEOMETRY produced proportion Q. E. D. THEOREM Q. E. F. PROBLEM quadrilateral radii radius rectangle regular inscribed regular polygon respectively equal rhombus right angles right-angled triangle SCHOLIUM secant similar polygons square Subtract tangent third side trapezoid triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 14 - Things which are equal to the same thing, are equal to each other. 2. If equals are added to equals, the sums are equal. 3. If equals are subtracted from equals, the remainders are equal. 4. If equals are added to unequals, the sums are unequal.
Σελίδα 83 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 85 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 44 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Σελίδα 14 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.
Σελίδα 136 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 123 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 55 - A polygon of three sides is a triangle ; of four, a quadrilateral; of five, a pentagon ; of six, a hexagon ; of seven, a heptagon; of eight, an octagon; of nine, a nonagon; of ten, a decagon; of twelve, a dodecagon.
Σελίδα 137 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 177 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.