The Elements of Plane and Solid Geometry: With Chapters on Mensuration and Modern GeometryPorter & Coates, 1879 - 266 sider |
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Resultat 1-5 av 15
Side 16
... intersect each other cannot both be parallel to the same straight line . 12. The shortest distance between two points is the straight line which joins them . NOTE . - The student should carefully construct all the figures he uses in the ...
... intersect each other cannot both be parallel to the same straight line . 12. The shortest distance between two points is the straight line which joins them . NOTE . - The student should carefully construct all the figures he uses in the ...
Side 18
... ively equal to A , B , C. Scholium . - In practice we need not describe the whole circle . Two small arcs intersecting at G will be sufficient . Corollary . - If the triangle is to be equilateral 18 GEOMETRY . — BOOK I.
... ively equal to A , B , C. Scholium . - In practice we need not describe the whole circle . Two small arcs intersecting at G will be sufficient . Corollary . - If the triangle is to be equilateral 18 GEOMETRY . — BOOK I.
Side 50
... intersect in the same point . 33. One of the angles of a parallelogram is three halves of a right angle . What are the values of the others in parts of a right angle ? in degrees ? 34. One of the exterior angles of an equilateral figure ...
... intersect in the same point . 33. One of the angles of a parallelogram is three halves of a right angle . What are the values of the others in parts of a right angle ? in degrees ? 34. One of the exterior angles of an equilateral figure ...
Side 59
... intersect each other in E ; and because the vertical angles AED , CEB are equal ( I. 17 ) , and also the alternate angles EAD , ECB ( I. 27 ) , the triangles AED , CEB have two A B angles of each equal , and the sides AD , BC are equal ...
... intersect each other in E ; and because the vertical angles AED , CEB are equal ( I. 17 ) , and also the alternate angles EAD , ECB ( I. 27 ) , the triangles AED , CEB have two A B angles of each equal , and the sides AD , BC are equal ...
Side 69
... equal lines are drawn to the cir- cumference BDF , H is the centre of BDF . Therefore the same point is the A B C centre of two circles which intersect , which is impossible ( III . 5 ) . Therefore the two circles GEOMETRY . - BOOK III .
... equal lines are drawn to the cir- cumference BDF , H is the centre of BDF . Therefore the same point is the A B C centre of two circles which intersect , which is impossible ( III . 5 ) . Therefore the two circles GEOMETRY . - BOOK III .
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Vanlige uttrykk og setninger
A-BCD AB² ABCD altitude angle ABC angle ACB angle BAC apothem bisect centre of similitude chord circle ABC circumference cone Corollary cylinder decagon describe diagonals diameter divided draw equal angles equiangular feet figure four right angles frustum given circle given straight line greater Hence inscribed interior angles intersect isosceles Let ABC line joining lune meet middle point multiplied number of sides opposite angles parallelogram parallelopiped pass perimeter perpendicular plane pole polyedron prism produced Prop proportional Proposition 12 Proposition 13 pyramid quadrilateral radical axis radii radius rectangle contained regular polygon right angles Scholium segment semicircle similar similar triangles slant height solid solid angle sphere spherical triangle square surface symmetrical tangent Theorem Theorem.-If three sides triangle ABC vertex
Populære avsnitt
Side 53 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 81 - On a given straight line to describe a segment of a circle, containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and...
Side 31 - Any two angles of a triangle are together less than two right angles.
Side 128 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 15 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals the wholes are equal. 3. If equals be taken from equals the remainders are equal.
Side 82 - To cut off a segment from a given circle which shall contain an angle equal to a given rectilineal angle. Let ABC be the given circle, and D the given rectilineal angle ; it is required to cut off a segment from the circle ABC that shall contain an angle equal to the given angle D.
Side 62 - If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section.
Side 166 - A be a solid angle contained by any number of plane angles BAC, CAD, DAE, EAF, FAB: these together are less than four right angles. Let the planes...
Side 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.
Side 120 - Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.