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76. What is a plane surfece ? Polygonal ? Curved ? 77. What is the superficial unit? Why selected ? 78. What is the meaning of area ? 79. What is the area of a right parallelogram? 80. What is the area of a square ? 81. What is the area of any parallelogram ? Why? 82. What is the area of a triangle? Why? 83. What is the area of a trapezoid ? Why? 84. What is the area of a regular polygon? Why? 85. What is the area of a circle? Why? 86. What is the area of a sector ? Segment? Why? 87. How do you find the area of an irregular polygon?

Can it be converted into an equivalent triangle? 88. What is demonstrated of the square of the hypothe

puse ? 89. Can you make a square equivalent to the sum or dif

ference of two given squares ? 90. Can you make a parallelogram equivalent to a given

square, and having the sum or difference of its base and

altitude equal to a given line ? 91. Can you make a square which shall be to a given

square, in any given ratio? 92. Can you find the exact ratio of the circumference of

a circle to its diameter ? 93. Can you find an approximate ratio ? 94. What is it? Could the approximation be carried fur

ther? 95. How do you find the circumference from the diame

ter? How the diameter from the circumference ? 96. How do you find the area from the radius ? 97. What Greek character is used to express the above

ratio? 98. Can you make a square equivalent to any given fig

ure? How? Why? 99. How are surfaces compared ? 100. How are similar figures compared ? What is their

ratio ? 101. What is the ratio of two circles ? 102. Do'equal perimeters always enclose equal areas ?

How is this proved ? 103. Among triangles of the same base and equal perim-,

eters, which is the greatest ?

104. Among polygons of the same perimeter and number

of sides, which is the greatest? 105. Among polygons of equal perimeters and equal + sides, which is the greatest? 106. Among regular polygons of the same perimeter,

which is greatest ? Why? 107. Is a circle greater than any polygon of the same pe

rimeter? Why? 108. How is the position of a plane determined ? 109. What is the intersection of two planes ? 110. How are plane angles measured? 111. Do they have the same properties as linear angles ? 112. When is a line perpendicular to a plane ? 113. What measures the distance from a point to a plane?"

. 114. When are two planes, or a line and a plane, par

allel ? 115. What is proved of parallel lines comprehended be

tween parallel planes ? 116. What is proved of the intersections of two parallel

planes by a third ? 117. What is proved of straight lines drawn between three

parallel planes ? 118. What is a Solid ? How generated ? Boundaries ? 119. What is a polyedron? What is the side or edge ? 120. What are the planes which bound it called ? 121. What is a prism? Its bases ? Altitude ? Convex sur

face? What is a right prism ? 122. What is a parallelopiped ? Right parallelopiped ? 123. What is a cube? 124. What is a pyramid ? Base ? Altitude ? Convex sur

face? 125. What is a regular pyramid ? Frustum of a pyramid ? 126. What are the three round bodies ? 127. What is a Cylinder ? Base ? Altitude ? Convex sur

face? 128. What is a cone? Vertex ? Altitude ? Convex sur

face? 129. What is the side of a cone? What is the frustum of

a cone? 130. What is a sphere? How generated ? 131. What is every section made in the sphere? 132. What is a great circle? What a small one? 133. What is a spherical sector ? Spherical segment?

[graphic]

134. What is the altitude of the sector or segment? 135. What is a zone? Its altitude ? 136. How do you find the surface of a prism? 137. How do you find the surface of a pyramid ? 138. How do you find the surface of the frustum of a pyr

amid ? 139. What is taken for the unit of solidity? Why? 140. What is the solidity of a right parallelopiped ? 141. What is the solidity of a cube? 142. What is the solidity of any parallelopiped ? Why? 143. What is the solidity of a right triangular prism? Why? 144. What of any triangular prism ? Of any prism? Why? 145. What is the solidity of a triangular pyramid? Why? 146. What is the solidity of any pyramid ? Why? 147. What is the solidity of the frustum of a pyramid ? 148. What is the solidity of a truncated triangular prism? 149. What is the surface of a cylinder ? Convex surface? 150. What is the surface of a cone? Convex surface ? 151. What is the surface of the frustum of a cone? Con

vex surface ? 152. What is the surface of a sphere ? Of a zone? 153. What ratio does the surface of an inscribed sphere

bear to that of a circumscribed cylinder? 154. What is the solidity of a cylinder? Why? 155. What is the solidity of a cone? Why? 156. What is the solidity of the frustum of a cone? Why? 157. What is the solidity of a sphere? Why? 158. What is the solidity of a spherical sector ? 159. What ratio does the solidity of an inscribed sphere

bear to that of a circumscribed cylinder ? 160. How do you find the solidity of a spherical segment

of one base? Of two bases ? 161. How are solids compared ? 162. What is the ratio of the surfaces of two spheres ? 163. What is the ratio of the solidities of two spheres ? 164. What are similar polyedrons ? 165. What are similar cones and cylinders ?

166. What is the ratio of two similar pyramids ? 167. What is the ratio of two similar polyedrons ?

168. What is the ratio of two similar cones or cylinders ?

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