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 39
... rectangle ( c ) , whose angles are all equal and therefore right angles . 4th . The square ( d ) , whose sides are all equal and whose angles are all equal . The square is at once a rhombus and a rectangle . α b с d PROPOSITION XXX ...
... rectangle ( c ) , whose angles are all equal and therefore right angles . 4th . The square ( d ) , whose sides are all equal and whose angles are all equal . The square is at once a rhombus and a rectangle . α b с d PROPOSITION XXX ...
Σελίδα 42
... rectangle are equal . Let ABCD be a rectangle ; then its diagonals , AC and BD , are equal . For , the right triangles ABC and DCB are equal ( 76 ) ; therefore , ACBD . 115. Corollary I. The diagonals of a square are equal , and , since ...
... rectangle are equal . Let ABCD be a rectangle ; then its diagonals , AC and BD , are equal . For , the right triangles ABC and DCB are equal ( 76 ) ; therefore , ACBD . 115. Corollary I. The diagonals of a square are equal , and , since ...
Σελίδα 85
... rectangle , and the angles at A and A ' are right angles . Hence , AA ' is a tangent to both circles . Since two tangents can be drawn from O ' to the circle OM , there are two exterior common tangents to the given circles , namely , AA ...
... rectangle , and the angles at A and A ' are right angles . Hence , AA ' is a tangent to both circles . Since two tangents can be drawn from O ' to the circle OM , there are two exterior common tangents to the given circles , namely , AA ...
Σελίδα 126
... rectangles having equal altitudes are to each other as their bases . Let ABCD , AEFD , be two rectangles hav- ing equal ... rectangle ABCD will be divided into 7 equal rectangles ( I. 120 ) , of which AEFD 126 BOOK IV COMPARISON AND ...
... rectangles having equal altitudes are to each other as their bases . Let ABCD , AEFD , be two rectangles hav- ing equal ... rectangle ABCD will be divided into 7 equal rectangles ( I. 120 ) , of which AEFD 126 BOOK IV COMPARISON AND ...
Σελίδα 127
... rectangles having equal bases are to each other as their altitudes . Note . In these propositions , by " rectangle " is to be understood " surface of the rectangle . " PROPOSITION II . - THEOREM . 5. Any two rectangles are to each other ...
... rectangles having equal bases are to each other as their altitudes . Note . In these propositions , by " rectangle " is to be understood " surface of the rectangle . " PROPOSITION II . - THEOREM . 5. Any two rectangles are to each other ...
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.