The First Six Books of the Elements of Euclid: And Propositions I-XXI of Book XI, and an Appendix on the Cylinder, Sphere, Cone, Etc., with Copious Annotations and Numerous ExercisesHodges, Figgis, & Company, 1885 - 312 sider |
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Resultat 1-5 av 12
Side 108
... concyclic . XIV . A cyclic quadrilateral is one which is inscribed in a circle . xv . It will be proper to give here an explanation of the extended meaning of the word angle in Modern Geometry . This extension is necessary in Trigono ...
... concyclic . XIV . A cyclic quadrilateral is one which is inscribed in a circle . xv . It will be proper to give here an explanation of the extended meaning of the word angle in Modern Geometry . This extension is necessary in Trigono ...
Side 133
... inscribed in a circle it is a rectangle . Exercises . 1. If the opposite angles of a quadrilateral be supplemental , it is cyclic . 2. If a figure of six sides be inscribed in a circle , the sum of any three alternate angles is four ...
... inscribed in a circle it is a rectangle . Exercises . 1. If the opposite angles of a quadrilateral be supplemental , it is cyclic . 2. If a figure of six sides be inscribed in a circle , the sum of any three alternate angles is four ...
Side 141
... inscribed in a circle , its diagonals intersect at the centre of the circle . Cor . 2. - Find the centre of a circle by ... quadrilateral ABCD is cyclic , the sum of the opposite angles ABC , CDA is two right angles [ XXII . ] , and ...
... inscribed in a circle , its diagonals intersect at the centre of the circle . Cor . 2. - Find the centre of a circle by ... quadrilateral ABCD is cyclic , the sum of the opposite angles ABC , CDA is two right angles [ XXII . ] , and ...
Side 151
... concyclic points ? 11. What is a cyclic quadrilateral ? 12. How many intersections can a line and a circle have ? 13. What does the line become when the points of intersection become consecutive ? 14. How many points of intersection can ...
... concyclic points ? 11. What is a cyclic quadrilateral ? 12. How many intersections can a line and a circle have ? 13. What does the line become when the points of intersection become consecutive ? 14. How many points of intersection can ...
Side 153
... cyclic quadrilateral intersect again in four concyclic points . 8. The four angular points of a cyclic quadrilateral determine four triangles whose orthocentres ( the intersections of their per- pendiculars ) form an equal quadrilateral ...
... cyclic quadrilateral intersect again in four concyclic points . 8. The four angular points of a cyclic quadrilateral determine four triangles whose orthocentres ( the intersections of their per- pendiculars ) form an equal quadrilateral ...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ... Euclid,John Casey Uten tilgangsbegrensning - 1885 |
Vanlige uttrykk og setninger
ABCD AC is equal adjacent angles altitude angle ABC angle ACB angle BAC angular points Axiom bisector bisects centre chord circles touch circumference circumscribed circle collinear concurrent lines const coplanar cyclic quadrilateral Dem.-Let diagonals diameter divided draw equal angles equal to AC equiangular equilateral triangle escribed circles Euclid Exercises exterior angle Geometry given circle given line given point greater Hence the angle hypotenuse inscribed less line AC line joining locus manner meet middle points multiple nine-points circle opposite sides parallel parallelogram parallelopiped perpendicular plane points of intersection prism PROP Proposition prove radii radius rectangle contained rectilineal figure regular polygon respectively equal right angles right line segments semicircle sides AC similar square on AC tangent theorem triangle ABC vertex vertical angle
Populære avsnitt
Side 299 - Thus the proposition, that the sum of the three angles of a triangle is equal to two right angles, (Euc.
Side 186 - When of the equimultiples of four magnitudes (taken as in the fifth definition) the multiple of the first is greater than that of the second, but the multiple of the third is not greater than the multiple of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the fourth...
Side 9 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 104 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Side 124 - The diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which...
Side 230 - If from any angle of a triangle, a straight line be drawn perpendicular to the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Side 29 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 63 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 128 - The diagonals of a quadrilateral intersect at right angles. Prove that the sum of the squares on one pair of opposite sides is equal to the sum of the squares on the other pair.
Side 22 - ACB, DB is equal to AC, and BC common to both ; the two sides DB, BC, are equal to the two AC, CB, each to each, and the angle DBC is equal to the angle ACB : therefore, the base DC is equal to the base AB, and the triangle DBC (Mr. Southey) is equal to the triangle ACB, the less to the greater, which is absurd,