A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry |
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Page 72
... inscribed angle is one whose vertex is on the circumference and whose sides are chords ; as BAC . In general , any rectilinear figure , as ABC , is said to be inscribed in a circle , when its angular points are on the circumference ...
... inscribed angle is one whose vertex is on the circumference and whose sides are chords ; as BAC . In general , any rectilinear figure , as ABC , is said to be inscribed in a circle , when its angular points are on the circumference ...
Page 73
... angle BOC , at the centre , is measured by the arc BC ( 53 ) ; therefore , the angle OAC is measured by one - half the arc BC . 2d . Let the centre of the circle fall within the inscribed angle BAC ; then , the measure of the angle BAC ...
... angle BOC , at the centre , is measured by the arc BC ( 53 ) ; therefore , the angle OAC is measured by one - half the arc BC . 2d . Let the centre of the circle fall within the inscribed angle BAC ; then , the measure of the angle BAC ...
Page 74
... angle BAC , inscribed in a segment greater than a semicircle , is acute ; for it is measured by half the arc BDC , which is less than a semi - circumference . Any angle BDC , inscribed in a segment less than a semicircle , is obtuse ...
... angle BAC , inscribed in a segment greater than a semicircle , is acute ; for it is measured by half the arc BDC , which is less than a semi - circumference . Any angle BDC , inscribed in a segment less than a semicircle , is obtuse ...
Page 77
... angle ECD , inscribed in a semicircle , is a right angle ( 59 ) . This construction is often preferable to the preceding , especially when the given point C is at , or near , one extremity of the given line , and it is not convenient to ...
... angle ECD , inscribed in a semicircle , is a right angle ( 59 ) . This construction is often preferable to the preceding , especially when the given point C is at , or near , one extremity of the given line , and it is not convenient to ...
Page 83
... angle is the greatest angle of a triangle ( I. 70 ) , and the side opposite to it must be the greatest side ( I. 92 ) ... inscribed ( 56 ) . PROPOSITION XXXVIII . - PROBLEM . 89. At a given BOOK II . 83.
... angle is the greatest angle of a triangle ( I. 70 ) , and the side opposite to it must be the greatest side ( I. 92 ) ... inscribed ( 56 ) . PROPOSITION XXXVIII . - PROBLEM . 89. At a given BOOK II . 83.
Other editions - View all
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2016 |
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... William Chauvenet No preview available - 2015 |
Common terms and phrases
ABCD AC² adjacent angles altitude apothem base bisects centre of similitude chord circumference circumscribed coincide common cone 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 hypotenuse indefinitely inscribed angle isosceles Let ABC measure medial lines 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
Popular passages
Page 128 - The area of a rectangle is equal to the product of its base and altitude.
Page 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...
Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 79 - 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.
Page 29 - The sum of the three angles of any triangle is equal to two right angles.
Page 175 - If a straight line is perpendicular to each of two straight lines at' their point of intersection, it is perpendicular to the plane of those lines.
Page 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 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.
Page 197 - A right prism is a prism •whose lateral edges are perpendicular to the planes of the bases.
Page 127 - Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R...