Plane and Solid GeometryLongmans, Green and Company, 1898 - 210 σελίδες |
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Σελίδα vi
... given as exercises or as corollaries . - Until within the past two decades the verbiage of demon- strations was so elaborate that the student was tempted to memorize . The natural reaction resulted , and for a while our authors passed ...
... given as exercises or as corollaries . - Until within the past two decades the verbiage of demon- strations was so elaborate that the student was tempted to memorize . The natural reaction resulted , and for a while our authors passed ...
Σελίδα 3
... Given Axiom ( Assumed truth ) Proposition Postulate ( Assumed possibility ) That something can be done Problem AXIOMS . 28. 1. Things which are equal to the same thing are equal to each other . 2. If equals be multiplied or divided by ...
... Given Axiom ( Assumed truth ) Proposition Postulate ( Assumed possibility ) That something can be done Problem AXIOMS . 28. 1. Things which are equal to the same thing are equal to each other . 2. If equals be multiplied or divided by ...
Σελίδα 7
... given angle . Thus , ABD is the comple- ment of the angle DBC ; also DBC is the complement of the angle ABD . 41. The Supplement of an angle is the difference between a straight angle and the given angle . Thus , ACD is the sup- plement ...
... given angle . Thus , ABD is the comple- ment of the angle DBC ; also DBC is the complement of the angle ABD . 41. The Supplement of an angle is the difference between a straight angle and the given angle . Thus , ACD is the sup- plement ...
Σελίδα 8
... given point on the same side of a straight line BF , is equal to two right B- angles . For their sum is equal to the C A F sum of the angles EAB and EAF ; which , from the proposition just demonstrated , is equal to two right angles ...
... given point on the same side of a straight line BF , is equal to two right B- angles . For their sum is equal to the C A F sum of the angles EAB and EAF ; which , from the proposition just demonstrated , is equal to two right angles ...
Σελίδα 9
James Howard Gore. E D 47. COR . 3. At a given point in a straight line , and on a given side of the line , only one per- pendicular to that line can be erected . For if two could be erected , let them be EC and DC ; then ( by 35 ) ...
James Howard Gore. E D 47. COR . 3. At a given point in a straight line , and on a given side of the line , only one per- pendicular to that line can be erected . For if two could be erected , let them be EC and DC ; then ( by 35 ) ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC² acute angle AD² adjacent adjacent angles altitude angle formed angles are equal apothem arc BC base and altitude bisect bisector called centre chord circumference circumscribed cone cylinder diagonals diameter diedral angles distance divided draw drawn ECDH equally distant equilateral equivalent EXERCISES faces four right angles frustum given point given straight line hence homologous homologous sides hypotenuse inscribed polygon interior angles intersection isosceles triangle join lateral area lateral edges Let ABC lune mean proportional measured by one-half middle point number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron PROPOSITION XI prove pyramid Q.E.D. PROPOSITION quadrilateral radii radius ratio rectangle rectangular parallelopiped regular polygon right triangle SCHOLIUM segments semiperimeter sphere spherical angle spherical polygon spherical triangle surface tangent THEOREM triangle ABC triangles are equal triangular triangular prism V-ABC vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 46 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Σελίδα 105 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Σελίδα 82 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Σελίδα 192 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 108 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Σελίδα 146 - A STRAIGHT line is perpendicular to a plane, when it is perpendicular to every straight line which it meets in that plane.
Σελίδα 30 - In an isosceles triangle, the angles opposite the equal sides are equal.
Σελίδα 80 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 79 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion. Let ad = ос.
Σελίδα 148 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.