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 15
... Corollary I. If one of the two adjacent angles which one line makes with another is a right angle , the other is also a right angle . 13. Corollary II . If a line CD is perpen- dicular to another line AB , then , reciprocally , the line ...
... Corollary I. If one of the two adjacent angles which one line makes with another is a right angle , the other is also a right angle . 13. Corollary II . If a line CD is perpen- dicular to another line AB , then , reciprocally , the line ...
Σελίδα 18
... Corollary I. The straight line EOF which bisects the angle AOC also bisects its vertical angle BOD . For , the angle FOD is equal to its vertical angle EOC , and FOB is equal to its vertical angle EOA ; therefore if EOC and EOA are ...
... Corollary I. The straight line EOF which bisects the angle AOC also bisects its vertical angle BOD . For , the angle FOD is equal to its vertical angle EOC , and FOB is equal to its vertical angle EOA ; therefore if EOC and EOA are ...
Σελίδα 20
... Corollary . The angles PDC and PEC are equal ; that is , two equal straight lines from a point to a straight line make equal acute angles with that line . 32. Definition . A broken line , as ABCDE , is called convex , when no one of its ...
... Corollary . The angles PDC and PEC are equal ; that is , two equal straight lines from a point to a straight line make equal acute angles with that line . 32. Definition . A broken line , as ABCDE , is called convex , when no one of its ...
Σελίδα 21
... Corollary I. ( Converse of Proposition VII . ) . Two equal ob- lique lines cut off equal distances from the perpendicular . 37. Corollary II . ( Converse of Proposition IX . ) . Of two unequal oblique lines , the greater cuts off the ...
... Corollary I. ( Converse of Proposition VII . ) . Two equal ob- lique lines cut off equal distances from the perpendicular . 37. Corollary II . ( Converse of Proposition IX . ) . Of two unequal oblique lines , the greater cuts off the ...
Σελίδα 22
... Corollary . Every point equally distant from the extremities of a straight line lies in the perpendicular erected at the middle of the line . 40. Definition . A geometric locus is the assemblage of all the points which possess a common ...
... Corollary . Every point equally distant from the extremities of a straight line lies in the perpendicular erected at the middle of the line . 40. Definition . A geometric locus is the assemblage of all the points which possess a common ...
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.