Elementary GeometryJ.B. Lippincott Company, 1893 |
From inside the book
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Page 15
... dicular AD let fall from the vertex upon the base is then called the altitude of the triangle . D 7. Definition . Equal figures are figures which can be made . to coincide throughout if one is properly superposed upon the other ...
... dicular AD let fall from the vertex upon the base is then called the altitude of the triangle . D 7. Definition . Equal figures are figures which can be made . to coincide throughout if one is properly superposed upon the other ...
Page 28
... dicular can be drawn to the line , and but one . Let AB be the given line and P the given point . Take a second line DE , and at some point F of DE let a perpendicular be erected ( Proposition I. ) . Superpose this second figure upon ...
... dicular can be drawn to the line , and but one . Let AB be the given line and P the given point . Take a second line DE , and at some point F of DE let a perpendicular be erected ( Proposition I. ) . Superpose this second figure upon ...
Page 29
... from the given point , are equal . 2. Theorem . Two equal oblique lines drawn from a point to a line meet it at equal distances from the foot of the perpen- dicular . PROPOSITION XVIII . — THEOREM . 34. If a perpendicular 3 * BOOK I. 29.
... from the given point , are equal . 2. Theorem . Two equal oblique lines drawn from a point to a line meet it at equal distances from the foot of the perpen- dicular . PROPOSITION XVIII . — THEOREM . 34. If a perpendicular 3 * BOOK I. 29.
Page 30
... dicular is unequally distant from A and B. For , Q being on one side or the other of the perpendicular , one of the lines QA , QB must cut the perpendicular ; let it C B be QA and let it cut in P ; join PB . The straight line QB is less ...
... dicular is unequally distant from A and B. For , Q being on one side or the other of the perpendicular , one of the lines QA , QB must cut the perpendicular ; let it C B be QA and let it cut in P ; join PB . The straight line QB is less ...
Page 31
... the bisector in some point P ; from P let PF be drawn perpen- dicular to AC , and join QF . We have QH < QF ; also QF < QP + PF , or QF < QP + PE , or QF < QE ; there fore QHQE . D When the angle BAC is obtuse , the point BOOK I. 31.
... the bisector in some point P ; from P let PF be drawn perpen- dicular to AC , and join QF . We have QH < QF ; also QF < QP + PF , or QF < QP + PE , or QF < QE ; there fore QHQE . D When the angle BAC is obtuse , the point BOOK I. 31.
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - 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 131 - 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.
Page 245 - 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 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.