Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith1876 - 349 páginas |
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Página xii
... MULTIPLES AND EQUIMULTIPLES - Pp . 211 to 214 . DEFINITIONS I. II . . POSTULATE • METHOD OF NOTATION SCALES OF MULTIPLES AXIOMS . Note 1 • PROPOSITION I. ( EUCL . V. 1 ) PROPOSITION II . ( EUCL . V. 2 ) . · 211 • · 211 · · · 211 · 212 ...
... MULTIPLES AND EQUIMULTIPLES - Pp . 211 to 214 . DEFINITIONS I. II . . POSTULATE • METHOD OF NOTATION SCALES OF MULTIPLES AXIOMS . Note 1 • PROPOSITION I. ( EUCL . V. 1 ) PROPOSITION II . ( EUCL . V. 2 ) . · 211 • · 211 · · · 211 · 212 ...
Página 211
Euclides, James Hamblin SMITH. BOOK V. SECTION I. On Multiples and Equimultiples . DEF . I. A GREATER magnitude is a Multiple ... multiple of a greater magnitude , when the less is contained an exact number of times in the greater . These ...
Euclides, James Hamblin SMITH. BOOK V. SECTION I. On Multiples and Equimultiples . DEF . I. A GREATER magnitude is a Multiple ... multiple of a greater magnitude , when the less is contained an exact number of times in the greater . These ...
Página 215
... multiple of B can be found , such that it would occupy the same place among the multiples of A , which is occupied by some one of the multiples of A ; that is , this particular multiple of B represents the same magnitude as that , which ...
... multiple of B can be found , such that it would occupy the same place among the multiples of A , which is occupied by some one of the multiples of A ; that is , this particular multiple of B represents the same magnitude as that , which ...
Página 217
... multiple of the first is greater than that of the second , the multiple of the third is greater than that of the fourth , and when the multiple of the first is equal to that of the second , the multiple of the third is equal to that of ...
... multiple of the first is greater than that of the second , the multiple of the third is greater than that of the fourth , and when the multiple of the first is equal to that of the second , the multiple of the third is equal to that of ...
Página 218
... multiples of A and B in the Scale of Relation of A and B , is precisely the same as the order of the multiples of C and D in the Scale of Relation of C and D ; or , when every multiple of A is found in the same position among the multiples ...
... multiples of A and B in the Scale of Relation of A and B , is precisely the same as the order of the multiples of C and D in the Scale of Relation of C and D ; or , when every multiple of A is found in the same position among the multiples ...
Otras ediciones - Ver todas
Elements of Geometry, Containing Books I. to Vi.And Portions of Books Xi ... James Hamblin Smith,Euclides Sin vista previa disponible - 2022 |
Elements of Geometry, Containing Books I. to VI.and Portions of Books XI ... James Hamblin Smith,Euclides Sin vista previa disponible - 2018 |
Términos y frases comunes
ABCD angles equal angular points base BC BC=EF bisecting the angle centre chord circumference coincide diagonals diameter divided equal angles equal circles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given angle given circle given line given point given st given straight line greater than nD Hence inscribed isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram perpendicular produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius rectangle contained reflex angle required to describe rhombus right angles segment semicircle shew shewn straight line joining subtended sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Pasajes populares
Página 51 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 38 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 178 - 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.
Página 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon...
Página 50 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Página 104 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Página 187 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Página 89 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle, Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular AD from the opposite angle.
Página 5 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 5 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.