Plane and Solid GeometryAmerican Book Company, 1899 - 384 σελίδες |
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Σελίδα 19
... two points but one straight line can POSTULATES 1. A straight line may be produced indefinitely . A straight line may be drawn from any point to any o + plus , or increased by . - minus , GEOMETRY . Axioms · Postulates •
... two points but one straight line can POSTULATES 1. A straight line may be produced indefinitely . A straight line may be drawn from any point to any o + plus , or increased by . - minus , GEOMETRY . Axioms · Postulates •
Σελίδα 35
... how does it divide the supplementary adjacent angle formed by producing one side of the given angle through the vertex ? Proposition XVI 81. 1. Construct two angles whose corresponding sides PLANE GEOMETRY . — BOOK I. 35.
... how does it divide the supplementary adjacent angle formed by producing one side of the given angle through the vertex ? Proposition XVI 81. 1. Construct two angles whose corresponding sides PLANE GEOMETRY . — BOOK I. 35.
Σελίδα 36
... Produce BC and ED , if necessary , to intersect as at G. § 76 , Zr = v , and Zs = v ; .. Ax . 1 , r = 28 . § 59 , LsLs ' ; .. Ax . 1 , r = s ' . 2. § 55 , Zs + t2 rt . ; but < r = 2s ; < r + Zt = 2 rt . . Hence , § 32 , Zr and Zt are ...
... Produce BC and ED , if necessary , to intersect as at G. § 76 , Zr = v , and Zs = v ; .. Ax . 1 , r = 28 . § 59 , LsLs ' ; .. Ax . 1 , r = s ' . 2. § 55 , Zs + t2 rt . ; but < r = 2s ; < r + Zt = 2 rt . . Hence , § 32 , Zr and Zt are ...
Σελίδα 39
... produced , is called the Altitude of the triangle . Since any side of a triangle may be considered as its base , it is evident that a triangle may have three altitudes and that they will be unequal , if the sides of the triangle are ...
... produced , is called the Altitude of the triangle . Since any side of a triangle may be considered as its base , it is evident that a triangle may have three altitudes and that they will be unequal , if the sides of the triangle are ...
Σελίδα 41
... produced . Also , data , hence , LB = LE ; BC will take the direction of EF , and the point c will fall upon EF , or upon EF produced . Since the point c falls upon each of the lines DF and EF , it must fall upon their point of ...
... produced . Also , data , hence , LB = LE ; BC will take the direction of EF , and the point c will fall upon EF , or upon EF produced . Since the point c falls upon each of the lines DF and EF , it must fall upon their point of ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle formed angles are equal angles compare apothem arc intercepted base bisector bisects called central angle chord circle whose center circumference circumscribed compare in length Construct a triangle Data diagonals diameter dihedral angles distance divide equal circles equidistant equilateral triangle equivalent exterior extremities Find the locus frustum given line given point given straight line Hence homologous homologous sides hypotenuse inscribed angle interior angles intersecting isosceles trapezoid isosceles triangle line drawn measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane prism produced Proof proportion prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angles right triangle secant segment similar sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 103 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 147 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Σελίδα 65 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Σελίδα 45 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 62 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...
Σελίδα 59 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 81 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Σελίδα 45 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 31 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Σελίδα 88 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.