## Yale University Entrance Examinations in Mathematics: 1884 to 1898 |

### From inside the book

Results 1-5 of 18

Page 20

...

...

**theorems**possible when a perpen- dicular is let fall upon the hypothenuse of a right angled triangle from the opposite vertex . 4. Compute the area of a regular hexagon whose side is 5 feet . Construct a triangle of equivalent area . 5 ... Page 22

...

...

**theorem**of the cylinder ? 4. Define symmetrical spherical triangles and prove them equivalent . 5. The radii of the bases of a right circular cylinder and right circular cone are the same as a sphere's , say R. The altitudes of the cone ... Page 25

...

...

**theorem**to a cone . 3. Define symmetrical spherical triangles and show that they are equivalent . 4. Suppose a sphere of radius 5 ; upon a section of the sphere , at a distance 3 from the center , as a base , a cone is drawn whose ... Page 28

...

...

**theorem**when the point is inside the circle . 3. What is it to measure a quantity ? When are two magnitudes commensurable ; or incommensurable ? When a line is drawn parallel to any side of a triangle , show that it divides the other ... Page 34

...

...

**theorem**and proof on the area of a frustum of a regular pyramid . Give the**theorem**on the volume of a frustum of any pyramid . 4. A sphere circumscribes a cube whose edge is 5 inches ; get the surface and volume of the sphere , and ...### Common terms and phrases

binomial formula binomial theorem bisected chord circle circumference circumscribed common logarithm cone Construct continued fraction cosine Deduce Define Derive the formula Divide drawn Expand Express an angle expressions into factors feet Find the area Find the number Find the value following expressions fraction geometric geometric progression given points hypothenuse inches included angle inscribed JUNE line perpendicular locus loga method of undetermined number of terms parallelopiped perimeter perpendicular polyhedral angle polyhedrons prism pyramid QUADRATICS radians radii radius ratio regular polygons regular polyhedrons Resolve the following right angles secant segments SEPTEMBER series of ascending SHEFFIELD SCIENTIFIC SCHOOL Show similar polygons simplest form Simplify the following simultaneous equations sine SOLID AND SPHERICAL Solve the equation Solve the simultaneous sphere spherical triangle tangent tetrahedron theorem trigonometric functions undetermined coefficients vertex volume

### Popular passages

Page 173 - 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 4 - The sum of any two face angles of a trihedral angle is greater than the third face angle.

Page 190 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.

Page 125 - The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Page 115 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.

Page 171 - The area of a circle is equal to one-half the product of its circumference and radius.

Page 35 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.

Page 37 - In two polar triangles each angle of the one is the supplement of the opposite side in the other. Let ABC, A'B'C

Page 125 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 186 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.