A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern GeomentryJ.B. Lippincott & Company, 1871 - 368 σελίδες |
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Σελίδα 58
... can intersect in but two points ; for , they could not have a third point in common without having the same centre and becoming in fact but one circumference . TANGENTS AND SECANTS . F 23. Definitions . A tangent 58 GEOMETRY .
... can intersect in but two points ; for , they could not have a third point in common without having the same centre and becoming in fact but one circumference . TANGENTS AND SECANTS . F 23. Definitions . A tangent 58 GEOMETRY .
Σελίδα 59
... TANGENTS AND SECANTS . F 23. Definitions . A tangent is an indefinite straight line which has but one point in common ... tangent to the line AB at the point . C. A secant is a straight line which meets the circumference in two points ...
... TANGENTS AND SECANTS . F 23. Definitions . A tangent is an indefinite straight line which has but one point in common ... tangent to the line AB at the point . C. A secant is a straight line which meets the circumference in two points ...
Σελίδα 60
... tangent at that point ( 23 ) . 27. Corollary . Conversely , a tangent AB at any point C is perpen- dicular to the radius OC drawn to that point . For , if it were not perpendicular to the radius it would cut the circumference ( 25 ) ...
... tangent at that point ( 23 ) . 27. Corollary . Conversely , a tangent AB at any point C is perpen- dicular to the radius OC drawn to that point . For , if it were not perpendicular to the radius it would cut the circumference ( 25 ) ...
Σελίδα 61
... tangent is but one of the positions of our revolving line , it has properties in common with the secant ; and in order to exhibit such common properties in the most striking manner , it is often expedient to regard the tangent as a ...
... tangent is but one of the positions of our revolving line , it has properties in common with the secant ; and in order to exhibit such common properties in the most striking manner , it is often expedient to regard the tangent as a ...
Σελίδα 62
... tangents is a diameter . 31. Scholium 2. According to the principle of ( 28 ) , the tangent being regarded as a secant whose two points of intersection are coin- cident , the demonstration of the first case in the preceding theorem ...
... tangents is a diameter . 31. Scholium 2. According to the principle of ( 28 ) , the tangent being regarded as a secant whose two points of intersection are coin- cident , the demonstration of the first case in the preceding theorem ...
Άλλες εκδόσεις - Προβολή όλων
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone construct Corollary cylinder Definition denote diagonals diameter dicular diedral angle distance divided draw edges equally distant equilateral equivalent exterior angle faces figure find the locus frustum given circles given plane given point given straight line hence homologous indefinitely inscribed inscribed angle isosceles Let ABC measure middle point number of sides one-half opposite sides parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN plane passed polar pole polyedral angle polyedron prism PROPOSITION pyramid quadrilateral radical axis radii radius rectangle regular polygon respectively right angles right triangle Scholium secant segment similar sphere spherical polygon square straight line drawn straight line joining surface symmetrical tangent tetraedron theorem three given triangle ABC triedral vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 115 - X PB'; that is, if through a fixed point without a circle a tangent to the circle is drawn, and also any secant, the tangent is a mean proportional between the whole secant and its external segment.
Σελίδα 46 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Σελίδα 127 - The areas of two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 129 - The area of a parallelogram is equal to the product of its base and altitude. Let...
Σελίδα 117 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Σελίδα 219 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 261 - Any side of a spherical triangle is less than the sum of the other two.
Σελίδα 95 - If four quantities are in proportion, they are in proportion by composition, ie the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 132 - 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.