The Eclectic School Geometry: A Revision of Evan's School GeometryVan Antwerp, Bragg, 1884 - 155 páginas |
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Página 13
... side of a triangle to a point within the triangle , is the hypothesis . 10. When the conclusion of one proposition is taken as the hypothesis of another , each proposition is the converse of the other . Sch . 1. - For an illustration ...
... side of a triangle to a point within the triangle , is the hypothesis . 10. When the conclusion of one proposition is taken as the hypothesis of another , each proposition is the converse of the other . Sch . 1. - For an illustration ...
Página 17
... sides of the angle . Thus , BA and BC are the sides , and B the vertex , of the angle ABC ; or , as B A it may be read , the angle B. When two angles have a common ver- tex , and one side common , they are called adjacent angles . Thus ...
... sides of the angle . Thus , BA and BC are the sides , and B the vertex , of the angle ABC ; or , as B A it may be read , the angle B. When two angles have a common ver- tex , and one side common , they are called adjacent angles . Thus ...
Página 18
... side of it , are together equal to two right angles . A- 10 B Let the line OC move around the fixed point C so that OCB will constantly increase , and OCA as constantly decrease . In one position , as DC , these two angles must be equal ...
... side of it , are together equal to two right angles . A- 10 B Let the line OC move around the fixed point C so that OCB will constantly increase , and OCA as constantly decrease . In one position , as DC , these two angles must be equal ...
Página 19
... side of a straight line , their sum is two right angles . Cor . 2. At a given point , C , but one perpendicular can be erected to the line AB ( ? ) . ( See Def . 3. ) AB ( ? ) . THEOREM II . If two straight lines cut one another , the ...
... side of a straight line , their sum is two right angles . Cor . 2. At a given point , C , but one perpendicular can be erected to the line AB ( ? ) . ( See Def . 3. ) AB ( ? ) . THEOREM II . If two straight lines cut one another , the ...
Página 20
... sides parallel , each to each , and directed the same way from the vertex , they are equal . A E B A and B are the given angles . Prolong the line DB to N. Ang . B Ang . C ( ? ) . Complete . = Cor . 3. - If two angles have their sides ...
... sides parallel , each to each , and directed the same way from the vertex , they are equal . A E B A and B are the given angles . Prolong the line DB to N. Ang . B Ang . C ( ? ) . Complete . = Cor . 3. - If two angles have their sides ...
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Términos y frases comunes
allel altitude apothegm Axiom Bisect the angles Book chord circle circumference coincide cone construction convex surface diagonal diameter diedral divided draw drawn equal Theo equal to half equally distant equilateral triangle equivalent exterior angle figure frustum Geometry given angle given line given point given straight line half the product Hence hexagon homologous sides hypotenuse hypothesis inscribed inscribed angle intersection isosceles Let ABC measured by half mutually equiangular number of equal number of sides parallel parallelogram parallelopiped pendicular perimeter perpendicular plane polyedron prism Prove pyramid quadrilateral Ques radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle secant segment slant height sphere square tangent tetraedron THEOREM THEOREM XI third trapezoid trian triangles ABC triedral vertex
Pasajes populares
Página 104 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.
Página 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Página 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Página 42 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Página 107 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R
Página 147 - The areas of two triangles which have 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.
Página 140 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.
Página 50 - The area of a regular polygon is equal to half the product of its apothem and perimeter.
Página 141 - The altitude of a pyramid or cone is the perpendicular distance from the ve~rtex to the base.
Página 39 - The area of a rectangle is equal to the product of its base and altitude.